2023-24.1.2301 Sections 100 and 110

2023 – 2024 Fall Semester MATH 2301 Calculus I Sections 100 and 110

Campus: Ohio University, Athens Campus

Course Description: First course in calculus and analytic geometry with applications in the sciences and engineering. Includes basic techniques of differentiation and integration with applications including rates of change, optimization problems, and curve sketching; includes exponential, logarithmic and trigonometric functions. Calculus is the mathematical language used to describe and analyze change. The course emphasizes how this abstract language and its associated techniques provide a unified way of approaching problems originating in disparate areas of science, technology, and society, highlighting how questions arising in different fields are connected to the same fundamental mathematical ideas. No credit for both MATH 2301 and 1350 (always keep 2301).

Prerequisites: (B or better in MATH 1350) or (C or better in 1300 or 1322) or (Math placement level 3)

Meeting Times and Locations:

Section 100 is a Lecture Section, taught by Mark Barsamian.

Lecture Section 100 meets Mon Wed, Fri 8:35am – 9:30m in Morton Hall 235.

Associated to Lecture Section 100 are four Recitation Sections, led by Isaac Agyei

Recitation Section 101 meets Tue 8:00am – 8:55am in Morton 318
Recitation Section 102 meets Tue 9:30am – 10:25am in Ellis 107
Recitation Section 103 meets Tue 12:30pm – 1:25pm in Morton 122
Recitation Section 104 meets Tue 2:00pm – 2:555pm in Morton 318

Section 110 is a Lecture Section, taught by Mark Barsamian.

Lecture Section 110 meets Mon Wed, Fri 10:45am – 11:40am in Morton Hall 237.

Associated to Lecture Section 110 are four Recitation Sections, led by Kenny So

Recitation Section 111 meets Tue 9:30am – 10:25am in Morton 218
Recitation Section 112 meets Tue 11:00am – 11:55am in Ellis 107
Recitation Section 113 meets Tue 2:00pm – 2:55pm in Morton 126
Recitation Section 114 meets Tue 3:30pm – 4:25pm in Morton 122

Information about the Instructors:

Instructor for Lecture Sections 100 and 110: Mark Barsamian

Office Location: Morton 521
Office Hours: Mon, Wed, Fri 1:00pm – 2:00pm (No appointment necessary)
Office Phone: 740-593-1273
Email: barsamia@ohio.edu

Instructor for Recitation Sections 101, 102, 103, 104: Isaac Agyei

Office Location: Morton 532
Office Hours: Mon, Wed 3:00pm – 4:00pm (No appointment necessary)
Office Phone: XXX
Email: ia520320@ohio.edu

Instructor for Recitation Sections 111, 112, 113, 114: Kenny So

Office Location: Morton XXX
Office Hours: XXX (No appointment necessary)
Office Phone: XXX
Email: ks698620@ohio.edu

Special Needs: If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let Mark Barsamian know as soon as possible so that your learning needs may be appropriately met. You should also register with the Office of Student Accessibility Services to obtain written documentation and to learn about the resources they have available.

Final Exam Date: All Athens Campus Sections of MATH 2301 have a Common Final Exam on Thu Dec 14, 2023, from 2:30pm – 4:30pm in various Morton Hall rooms. (Room assignments will be made later.)

Syllabus: This web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next four portions of hidden content (Textbook Information, Exercises, Grading, Calendar) and then print this web page.

Textbook and WebAssign Information:

click to enlarge

Required Online Course Materials: Through a program called Inclusive Access , the University has negotiated with the publisher a special price for this course's Required Online Course Materials . On the first day of class, you will receive access to an an online system called WebAssign . The WebAssign system includes an eText version of the textbook and an online homework system . The cost of the Online Course Materials is a discounted Inclusive Access Price of $45 plus 7% Ohio sales tax, for a total of about $48.15. That cost will be automatically billed to your Ohio University Student Account. If you drop the course before the drop deadline (Fri, Sep 8, 2023), your student account will be credited for any amount billed. After you register, you will receive more information about the Inclusive Access program, including an option to "Opt Out" of participation in the program. To "Opt Out" means that your payment for the Online Course Materials is not handled by the Inclusive Access program. If you do that, you can still use the Online Course Materials, but in order to access them, you will be asked to make a credit card payment for the Retail Price of the materials. (Note that the Retail Price is $111 plus 7% ohio tax, for a total of about $118.77. That is significantly higher than the Inclusive Access Price.)

Optional Print Copy of the Textbook: Many students (and instructors) prefer reading printed textbooks rather than eTexts. Students in Ohio University MATH 2301 Sections 100 and 110 can purchase a print copy of the book at the College Bookstore (at the corner of Court Street and Union Street in Athens) for the discounted price of $33.50 + 7% Ohio sales tax, for a total of around $35.85. This is an extraordinarily low price for a print textbook, and you are strongly encouraged to buy the print copy. Note that your purchase of the print copy will be in addition to the Online Course Materials that you receive as part of the Inclusive Access program, described above. So if you do buy the print copy, your total expenditures will be $48.15 (for the Online Course Materials purchased through the Inclusive Access program) plus $35.85 (for the print copy of the textbook, purchased at the College Bookstore) for a total of $84. That is still an excellent price for course materials. The print copy is a loose-leaf book; its full description is:

Title: Essential Calculus, Early Transcendentals, Second Edition, Loose-Leaf Edition
Author: James Stewart
Publisher: Cengage (2012)
ISBN: 9780357005262
Available at: College Bookstore at the corner of Court Street and Union Street in Athens

Link to download a PowerPoint presentation with Instructions for Setting Up WebAssign: Link

Exercises:

Exercises for Fall 2023 MATH 2301 Sections 100 and 110 (Barsamian)
(from Stewart Essential Calculus Early Transcendentals 2nd Edition)
Your goal should be to write solutions to all 333 exercises in this list.

Printable PDF of the Exercise List

1.3 The Limit of a Function: 1, 5, 7, 10, 11, 12, 13, 15, 23, 33, 39
1.4 Calculating Limits: 5, 7, 10, 11, 17, 21, 23, 25, 27, 31, 33, 35, 38, 42, 49, 51, 55
1.5 Continuity: 3, 5, 7, 17, 19, 27, 33, 39, 43, 47
1.6 Limits Involving Infinity: 1, 5, 7, 9, 10, 13, 19, 21, 25, 29, 33, 35, 40, 41, 45, 49
2.1 Derivatives & Rates of Change: 1, 5, 9, 11, 15, 16, 18, 25, 27, 29, 31, 33, 35, 43, 47
2.2 The Derivative as a Function: 1, 3, 5, 9, 11, 13, 19, 20, 22, 23, 25, 33, 35, 39
2.3 Basic Differentiation Formulas: 1, 7, 9, 11, 13, 19, 27, 29, 31, 33, 35, 37, 39, 45, 50, 57, 69
2.4 The Product & Quotient Rules: 3, 5, 7, 13, 16, 17, 19, 21, 26, 27, 31, 34, 37, 41, 51, 55
2.5 The Chain Rule: 1, 7, 13, 14, 17, 21, 25, 35, 43, 47, 51, 55, 63, 64
2.6 Implicit Differentiation: 5, 7, 9, 11, 13, 19, 21
2.7 Related Rates: 4, 5, 11, 13, 15, 20, 23, 25, 27, 28, 31
2.8 Linear Approx & Differentials: 1, 5, 6, 11, 13, 17, 19, 21, 23
3.1 Exponential Functions: 1, 5, 7, 9, 13, 15, 16, 17, 27, 29, 30
3.2 Inverse Functions, Logarithms: 5, 7, 9, 11, 15, 17, 18, 22, 23, 25, 35, 36, 39, 67, 71, 76
3.3 Derivs of Log. & Exp. Functs.: 1, 3, 4, 6, 13, 20, 26, 31, 35, 41, 45, 55, 57
3.4 Exponential Growth & Decay: 1, 2, 3, 9, 13, 16
4.1 Maximum & Minimum Values: 5, 9, 18, 19, 21, 25, 29, 35, 39, 43, 47, 49
4.2 The Mean Value Theorem: 1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 25
4.3 Derivs. & Shapes of Graphs: 1, 5, 7, 10, 13, 15, 19, 23, 27, 35, 37, 45
4.4 Curve Sketching: 1, 9, 11, 13, 15, 19, 31, 34, 39
4.5 Optimization Problems: 2, 7, 11, 15, 17, 22, 25, 30, 37, 39, 53, 57
4.6 Newton's Method: 4, 7, 9, 11, 13
4.7 Antiderivatives: 1, 2, 7, 12, 13, 15, 20, 27, 38, 40, 47, 53, 55
5.1 Areas and Distances: 2, 3, 4, 5, 9, 13, 16, 18
5.2 The Definite Integral: 1, 3, 9, 11, 15, 25, 30, 33, 35, 39, 40, 44
5.3 Evaluating Definite Integrals: 3, 7, 11, 18, 26, 29, 49, 51, 56, 59, 61, 65, 69
5.4 The Fund. Thm. of Calculus: 1, 3, 5, 10, 15, 25, 27
5.5 The Substitution Rule: 7, 11, 13, 17, 19, 23, 26, 27, 33, 37, 39, 44, 50, 53, 55, 61

A Suggestion for Studying: Even though WebAssign does not require that you write stuff down, you will learn a lot by focusing on your writing. Furthermore, having good writing skills will really help when working on a written Quiz or Exam. Therefore, you should write down a complete solution to each problem before you type the answer into the answer box in WebAssign . Focus on the clarity and correctness of your written solution. Keep your written work organized in a notebook. Compare your written solutions to my written solutions in lectures. Find another student, or a tutor, or your Recitation Instructor, or Mark Barsamian, to look over your written work with you.

Grading:

Grading System for MATH 2301 Sections 100 and 110 (Barsamian) 2023 – 2024 Fall Semester

During the course, you will accumulate a Points Total of up to 1028 possible points .

WebAssign: 28 Assignments @ 1 point each = 28 points possible (Extra Credit points)
Recitation: 15 Tuesday Recitation Activities @ 5 points each = 75 points possible
Quizzes: Best 8 of 9 Quizzes @ 30 points each = 240 points possible
Exams: Best 2 of 3 Exams @ 220 points each = 440 points possible
Final Exam: 245 points possible

At the end of the semester, your Points Total will be divided by $1000$ to get a percentage, and then converted into your Course Letter Grade using the 90%, 80%, 70%, 60% Grading Scale described below.

Observe that the Total Possible Points is $1028$, but your points total is divided by $1000$ to get the percentage that is used in computing your course grade. This is because the $28$ points that can be earned by doing WebAssign Homework are considered Extra Credit Points .

The 90%, 80%, 70%, 60% Grading Scale is used on all graded items in this course, and is used in computing your Course Letter Grade .

A grade of A, A- means that you mastered all concepts, with no significant gaps.
- If $93\% \leq score $, then letter grade is A .
- If $90\% \leq score \lt 93\%$, then letter grade is A- .
A grade of B+, B, B- means that you mastered all essential concepts and many advanced concepts, but have some significant gap.
- If $87\% \leq score \lt 90\%$, then letter grade is B+ .
- If $83\% \leq score \lt 87\% $, then letter grade is B .
- If $80\% \leq score \lt 83\%$, then letter grade is B- .
A grade of C+, C, C- means that you mastered most essential concepts and some advanced concepts, but have many significant gaps.
- If $77\% \leq score \lt 80\%$, then letter grade is C+ .
- If $73\% \leq score \lt 77\%$, then letter grade is C .
- If $70\% \leq score \lt 73\%$, then letter grade is C- .
A grade of D+, D, D- means that you mastered some essential concepts.
- If $67\% \leq score \lt 70\%$, then letter grade is D+ .
- If $63\% \leq score \lt 67\% $, then letter grade is D .
- If $60\% \leq score \lt 63\%$, then letter grade is D- .
A grade of F means that you did not master essential concepts.
- If $0\% \leq score \lt 60\%$, then letter grade is F .

There is no grade curving in this course.

Two things that are not part of your Course Grade

Attendance: Attendance is recorded but is not part of your course grade
Written Solutions to Homework Exercises: There is a list of Homework Exercises on this web page. To succeed in the course, you will need to do lots of them (preferrably all of them), writing the solutions on paper. Those written solutions are not graded and are not part of your course grade. (Your scores on the online WebAssign homework will be part of your course grade.)

Grade Calculation Worksheet

Use this to calculate your Current Letter Grade before the Final Exam: Grade Calculation Worksheet

Attendance Policy:

Attendance is required for all class meetings, and your attendance (or absence) will be recorded, but attendance is not used in the calculation of your course grade.

Missing Class: If you miss a class for any reason, it is your responsibility to learn the stuff that you missed. You can do this by studying a classmate's notes, or reading the Lecture notes that Mark Barsamian posts online, and by reading the textbook. Your Instructurs will not use office hours to teach topics discussed in class meetings to students who were absent.

Missing a Quiz or Exam Because of Illness: If you are too sick to take a quiz or exam, then you must do these three things:

Send Mark Barsamian an e-mail before the quiz/exam, telling him that you are going to miss it because of illness. He will arrange for a date and time for a Make-Up quiz/exam. (Generally, the Make-up for a Friday quiz/exam needs to take place on the following Monday or Tuesday. Therefore, it is important to communicate with him right away.(
Go to the Hudson Student Health Center (or some other Medical Professional) to get examined.
Later, you will need to bring your Mark Barsamian your documentation from the Hudson Student Health Center (or a Medical Professional) showing that you were treated there.

Without those three things, you will not be given a make-up. (When you miss a Quiz or Exam and are not given a Make-Up, the missed Quiz or Exam will be considered your one Quiz or Exam score that gets dropped.)

(Observe that self-diagnosis of an illness is not a valid documentation of an illness. In other words, you can't just tell Mark Barsamian that you did not come to a Quiz or Exam because you were not feeling well, and expect to get a Make-Up Quiz or Exam. If you are too sick to come to a Quiz or Exam, then you should be sick enough to go to a medical professional to get diagnosed and treated.)

Missing Quizzes or Exams Because of University Activity: If you have a University Activity that conflicts with one of our quizzes or exams, you must contact Mark Barsamian well before the quiz or exam to discuss arrangements for a make-up. They will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying Mark Barsamian in advance, you will not be given a make-up.

Missing Quizzes or Exams Because of Religious Observation: The Ohio University Faculty Handbook states the following:

Students may be absent for up to three days each academic semester to take time off for reasons of faith or religious or spiritual belief system or participate in organized activities conducted under the auspices of a religious denomination, church, or other religious or spiritual organization. Faculty shall not impose an academic penalty because of a student being absent nor shall faculty question the sincerity of a student's religious or spiritual belief systems. Students are expected to notify faculty in writing of specific dates requested for alternative accommodations no later than fourteen days after the first day of instruction.

For MATH 2301, this means that if you will be missing any Fall 2023 Quizzes or Exams for religious reasons, and if you want to have a Make-Up Quiz/Exam, you will need to notify Mark Barsamian no later than Monday, September 11, 2023 . You and he will work out the dates/times of your Make-Up Quiz/Exam. (In general, if you are going to miss a Friday Quiz/Exam, your Ihe will schedule you for a Make-Up on the following Monday or Tuesday.)

Missing Presentations, Quizzes, or Exams Because of Personal Travel: This course meets on Mondays, Wednesdays and Fridays, and attendance is required. Your Personal Travel (to home for the weekend, or out of town for vacations, etc) should be scheduled to not conflict with those Monday/Wednesday/Friday meetings. If you miss a Recitation, Quiz, or Exam because of Personal Travel (not an Offical University Activity), you will not be given a make-up. (When you miss a Quiz or Exam and are not given a Make-Up, the missed Quiz or Exam will be considered your one Quiz or Exam score that gets dropped.)

Electronic Communication Policy (For both Students and Instructors):

Policy for Electronic communication between MATH 2301 Students and Instructors

Electronic communication between MATH 2301 Students and Instructors should be done using one of these two methods:
- The Official Ohio University e-mail system . That is, communications should use email addresses ending in @ohio.edu . In other words, send your emails from your OU e-mail account, and address them to a recipient's OU e-mail address. (Students: If you use the Blackboard system to send an email to your Instructor, this is automatically taken care of.)
- The Teams program. (Teams can be used for chat , voice calling , video calling , and video meetings . It is remarkably powerful.
Do not use a personal email address (such as a gmail address) when sending an email, and do not send emails to a personal email address (such as gmail).
Students and Instructors should not communicate via text messages.
Students and Instructors: It is your reponsibility to check your OU e-mail every day. (Students: If you are communicating with your Instructor about a time-sensitive issue, such as trying to schedule a Make-Up Quiz or Exam after an illness, your e-mail replies need to be swift. It is not acceptable to let days pass before replying to an important e-mail message, with your excuse being that you had not checked your OU email. If you do this, you will lose the opportunity to have a Make-Up Quiz or Exam.)
It is a good practice to use a descriptive Subject line such as Regarding MATH 2301 Section XXX on your email messages. That way, the recipient will know to give the email message high priority.
It is also a good practice to use a greeting such as Hi Elon, on your email messages, and to identify yourself in your message. And use a closing such as Thanks,
Jeff Bezos

Policy on Cheating:

If cheat on a quiz or exam, you will receive a zero on that quiz or exam and your Instructor will submit a report to the Office of Community Standards and Student Responsibility (CSSR).

If you cheat on another quiz or exam, you will receive a grade of F in the course and your Instructor will again submit a report to the CSSR.

Calendar:

Calendar for MATH 2301 Sections 100 and 110 (Barsamian) 2023 – 2024 Fall Semester

Printable PDF of the Calendar

Items in red are graded.

Mon Aug 28: Course Intro and Section 1.3: The Limit of a Function ( Lecture Notes )

Tue Aug 29: Recitation R01 : Diagnostic Test and Section 1.3: The Limit of a Function ( Sample Problems for Diagnostic Test ) ( Class Drill on Limits )

Wed Aug 30: Section 1.4: Calculating Limits ( Lecture Notes )( Handout of Limit Laws )

Fri Sep 1: Section 1.4: Calculating Limits ( Lecture Notes )

Mon Sep 4: Holiday

Tue Sep 5: Recitation R02 : Calculating Limits (Section 1.4)( Handout Using the Squeeze Theorem ) ( Squeeze Theorem Worksheet )

Students Solving Problems and Discussing Their Solutions

A pair of students will work together to write the solution of a Suggested Homework Problem on the blackboard or whiteboard. The emphasis should be on writing a very clear solution, with key steps explained. Write large and clear!

Multiple pairs of students should be able to work simultaneously. There may be two or three rounds. The Recitation Instructor will decide how best to choreograph the rounds. After one round of students has finished writing their solutions on the white boards, they will sit down and the Instructor will lead a discussion of the solutions on the board. The Instructor and the students in the class will talk about what is good and not so good in each solution. Then the boards will be erased and the next round of students will come to the board and write the solution to their problems.

Scoring: If a student (either alone or as part of a team of two students) presents a solution to their assigned problem on the white board, their R02 score will be 5/5. (For this Sep 5 Recitation, students will get 5/5 regardless of whether their solutions are correct. In the future, the scoring will be more stringent.) If they do not present a solution, their R02 score will be 0/5.

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Sep 5 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bansode,Ankita
Section 101 Student #3: Bedell,Paris
Section 101 Student #4: Beegan,Caden
Section 101 Student #5: Brandt,Roman
Section 101 Student #6: Earl,Claire-Michael
Section 101 Student #7: Eisnaugle,Ethan
Section 101 Student #8: Fogwe,Brandt
Section 101 Student #9: Frometa,Amelia
Section 101 Student #10: Jackson,Henry
Section 101 Student #11: Miller,Taylor
Section 101 Student #12: Robinson,Alana
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,
Section 101 Student #19: Unassigned,
Section 101 Student #20: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: Walsh,Carly
Section 102 Student #14: White,Anna
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,
Section 102 Student #19: Unassigned,
Section 102 Student #20: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Gilbert,Wyatt
Section 103 Student #4: Hains,Amanda
Section 103 Student #5: Hawley,Frank
Section 103 Student #6: Kennedy,Quinn
Section 103 Student #7: Martis,Steve
Section 103 Student #8: Mikin,Reilly
Section 103 Student #9: Winterton,Jacob
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,
Section 103 Student #19: Unassigned,
Section 103 Student #20: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:555pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,Joseph
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,
Section 104 Student #19: Unassigned,
Section 104 Student #20: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Mulholland-Flint,Austin
Section 111 Student #11: Ngum,Venessa
Section 111 Student #12: Pickens,Charlee
Section 111 Student #13: Pinson,Caroline
Section 111 Student #14: Rasmussen,Cubbie
Section 111 Student #15: Rodean,Alex
Section 111 Student #16: Sahr,Griffin
Section 111 Student #17: Sautter,Jack
Section 111 Student #18: Scudder,Braedon
Section 111 Student #19: Wright,Beck
Section 111 Student #20: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Lewis-Baranyai,Enzo
Section 112 Student #14: Massie,Olivia
Section 112 Student #15: Miller,Austy
Section 112 Student #16: Newton,Lilly
Section 112 Student #17: Shields,Julia
Section 112 Student #18: Smith,Kaitlyn
Section 112 Student #19: Whittington,Kelsey
Section 112 Student #20: Williams,Ava

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Sikora,Daniella
Section 113 Student #16: Slingluff,Cheyenne
Section 113 Student #17: Wenning,Luke
Section 113 Student #18: Unassigned,
Section 113 Student #19: Unassigned,
Section 113 Student #20: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Blore,Noah
Section 114 Student #4: Cox,Madelyn
Section 114 Student #5: Dubois,Aleke
Section 114 Student #6: Elliott,Maggie
Section 114 Student #7: Hartzell,Molly
Section 114 Student #8: Kezele,Ashley
Section 114 Student #9: Lampa,Andrew
Section 114 Student #10: Mcclellan,Alex
Section 114 Student #11: Mcdermitt,Brian
Section 114 Student #12: Meyer,Morgan
Section 114 Student #13: Morris,Chase
Section 114 Student #14: Mueller,Maddy
Section 114 Student #15: Nguyen,Jim
Section 114 Student #16: Raynewater,Ty
Section 114 Student #17: Smith,Riley
Section 114 Student #18: Sobey,Lily
Section 114 Student #19: Wall,Logan
Section 114 Student #20: Young,Kiefer

The Problems to Be Done in Tue Sep 5 Recitation Meetings

Limits that are Indeterminate Forms and that require no trick, just messy work

Students 1,2:
(This problem is Exercise 1.4#15, similar to Book Section 1.4 Example 2 and similar to an example done in class on Fri Sep 1)
Find the limit

$$\lim_{t\rightarrow -3}\frac{t^2-9}{2t^2+7t+3}$$

Students 3,4: (This problem is Exercise 1.4#17, similar to Book Section 1.4 Example 4)

$$\lim_{h\rightarrow 0}\frac{(-5+h)^2-25}{h}$$

Students 5,6: (This problem is Exercise 1.4#25, an example done in class on Fri Sep 1)

$$\lim_{x\rightarrow -4}\frac{\frac{1}{4}+\frac{1}{x}}{4+x}$$

Limits that Involve Rationalizing

Students 7,8:
(This problem is Exercise 1.4#21, similar to Book Section 1.4 Example 5 and similar to an example done in class on Fri Sep 1)
Find the limit

$$\lim_{h\rightarrow 0}\frac{\sqrt{9+h}-3}{h}$$

Students 9,10:
(This problem is Exercise 1.4#23, similar to Book Section 1.4 Example 5 and similar to an example done in class on Fri Sep 1)
Find the limit

$$\lim_{x\rightarrow 16}\frac{4-\sqrt{x}}{16x-x^2}$$

Limits that Involve Absolute Value

Students 11,12:
(This problem is Exercise 1.4#38, similar to Book Section 1.4 Example 7 and similar to an example done in class on Fri Sep 1)
Find the limit

$$\lim_{x\rightarrow -6}\frac{2x+12}{|x+6|}$$

Limits that Involve the Squeeze Theorem

Students 13,14: (1.4#33) Given that for all $x$, $$4x-9 \leq f(x) \leq x^2-4x+7$$ find the limit $$\lim_{x\rightarrow 4}f(x)$$

Students 15,16:
(This problem is Exercise 1.4#35, similar to Book Section 1.4 Example 9)
Show that

$$\lim_{x\rightarrow 0}x^2\cos{(20\pi x)}=0$$

Limits that Use Famous Fact that $$\lim_{x\rightarrow 0}\frac{\sin{(x)}}{x}=1$$

Students 17,18:
(This problem is Exercise 1.4#41, similar to Book Section 1.4 Example 10)
Find the limit

$$\lim_{x\rightarrow 0}\frac{\sin{(3x)}}{x}$$

Students 19,20:
(This problem is Exercise 1.4#51, similar to Book Section 1.4 Example 10)
Find the limit

$$\lim_{t\rightarrow 0}\frac{\tan{(6t)}}{\sin{(2t)}}$$

Wed Sep 6: Section 1.5: Continuity ( Lecture Notes )( Handout Using The Intermediate Value Theorem ) ( Intermediate Value Theorem Worksheets )

Fri Sep 8: Section 1.6: Limits Involving Infinity ( Lecture Notes )(Last Day to Drop Without a W)(Quiz Q1 )

Quiz Q1 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Three Problems, 10 points each, printed on front & back of one sheet of paper
- One problem based on Suggested Exercises from Section 1.3 .
- Two problems based on Suggested Exercises from Section 1.4 .

Mon Sep 11: Section 1.6 Limits: Involving Infinity ( Lecture Notes )

Tue Sep 12: Recitation R03 : Calculating Limits Involving Infinity (Section 1.6)

Students Solving Problems and Discussing Their Solutions

Scoring: If a student (either alone or as part of a team of two students) presents a solution to their assigned problem on the white board, their R02 score will be in the range 1/5 to 5/5 (depending on how whether they have prepared ahead of time). If they do not present a solution, their R02 score will be 0/5.

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Sep 5 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1 and #11: Allen,Daylen
Section 101 Student #2 and #12: Bansode,Ankita
Section 101 Student #3 and #13: Bedell,Paris
Section 101 Student #4: and #14: Beegan,Caden
Section 101 Student #5 and #15: Brandt,Roman
Section 101 Student #6 and #16: Earl,Claire-Michael
Section 101 Student #7 and #17: Eisnaugle,Ethan
Section 101 Student #8 and #18: Frometa,Amelia
Section 101 Student #9 and #19: Jackson,Henry
Section 101 Student #10 and #20: Miller,Taylor and Robinson,Alana

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1 and #15: Fritz,Ronan
Section 102 Student #2 and #16: Herrmann,Mary
Section 102 Student #3 and #17: Hoffman,Sidney
Section 102 Student #4 and #18: Hubbard,Grace
Section 102 Student #5 and #19: Lavender,Kinley
Section 102 Student #6 and #20: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: Walsh,Carly
Section 102 Student #14: White,Anna

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1 and #9: Alder,Ethan
Section 103 Student #2 and #10: Blower,Carsen
Section 103 Student #3 and #11: Hains,Amanda
Section 103 Student #4 and #12: Hawley,Frank
Section 103 Student #5 and #13: Kennedy,Quinn
Section 103 Student #6 and #14: Martis,Steve
Section 103 Student #7 and #15: Mikin,Reilly
Section 103 Student #8 and #16: Winterton,Jacob
Section 103 Student #17: Unassigned Challenge Problem: Who can do it?!?
Section 103 Student #18: Unassigned Challenge Problem: Who can do it?!?
Section 103 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 103 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 104 (meets Tue 2:00pm – 2:555pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,Joseph
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned
Section 104 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 104 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Mulholland-Flint,Austin
Section 111 Student #11: Ngum,Venessa
Section 111 Student #12: Pickens,Charlee
Section 111 Student #13: Rasmussen,Cubbie
Section 111 Student #14: Rodean,Alex
Section 111 Student #15: Sahr,Griffin
Section 111 Student #16: Sautter,Jack
Section 111 Student #17: Scudder,Braedon
Section 111 Student #18: Wright,Beck
Section 111 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 111 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Lewis-Baranyai,Enzo
Section 112 Student #14: Massie,Olivia
Section 112 Student #15: Miller,Austy
Section 112 Student #16: Newton,Lilly
Section 112 Student #17: Shields,Julia
Section 112 Student #18: Smith,Kaitlyn
Section 112 Student #19: Whittington,Kelsey
Section 112 Student #20: Williams,Ava

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Sikora,Daniella
Section 113 Student #16: Slingluff,Cheyenne
Section 113 Student #17: Wenning,Luke
Section 113 Student #18: Unassigned
Section 113 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 113 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Blore,Noah
Section 114 Student #4: Cox,Madelyn
Section 114 Student #5: Dubois,Aleke
Section 114 Student #6: Elliott,Maggie
Section 114 Student #7: Hartzell,Molly
Section 114 Student #8: Kezele,Ashley
Section 114 Student #9: Lampa,Andrew
Section 114 Student #10: Mcclellan,Alex
Section 114 Student #11: Mcdermitt,Brian
Section 114 Student #12: Meyer,Morgan
Section 114 Student #13: Morris,Chase
Section 114 Student #14: Mueller,Maddy
Section 114 Student #15: Nguyen,Jim
Section 114 Student #16: Raynewater,Ty
Section 114 Student #17: Smith,Riley
Section 114 Student #18: Sobey,Lily
Section 114 Student #19: Wall,Logan
Section 114 Student #20: Young,Kiefer

The Problems to Be Done in Tue Sep 12 Recitation Meetings

Students #1, 2:

Similar Problem from Exercise List: 1.6 #13
Similar Book Example: Section 1.6 Example 1 is similar to part (b)
Similar Class Example: Fri Sep 8 Example is similar to part (a) and (b)

We are interested in the following three limits: $$\lim_{x\rightarrow -3^-}\frac{x+2}{x+3} \\ \lim_{x\rightarrow -3^+}\frac{x+2}{x+3} \\ \lim_{x\rightarrow -3}\frac{x+2}{x+3}$$

Find the limits using the expanded definition of limit presented in Section 1.6 . That is, limits can now include the terminology and notation of infinity . The expanded definition of limit is used in Section 1.6 Example 2 . Show all details clearly and use correct notation.
What does the result of (a) tell you about the graph of the rational function?

Students #3,4:

Similar Problem from Exercise List: 1.6 #13
Similar Book Example: Section 1.6 Example 1 is similar to part (b)
Similar Class Example: Fri Sep 8 Example is similar to part (a) and (b)

We are interested in the following three limits: $$\lim_{x\rightarrow 5^-}\frac{x^2-5x+6}{x-5} \\ \lim_{x\rightarrow 5^+}\frac{x^2-5x+6}{x-5} \\ \lim_{x\rightarrow 5}\frac{x^2-5x+6}{x-5}$$

Find the limits using the expanded definition of limit presented in Section 1.6 . That is, limits can now include the terminology and notation of infinity . The expanded definition of limit is used in Section 1.6 Example 2 . Show all details clearly and use correct notation.
What does the result of (a) tell you about the graph of the rational function?

Students #5,6:

Similar Problem from Exercise List: Exercise 1.4#42 is similar to one of the limits in part (a) and (b)
Similar Book Example: Section 1.6 Example 1 is similar to one of the limits in part (b)
Similar Class Example:

We are interested in the following three limits: $$\lim_{x\rightarrow 0^-}\left(\frac{1}{x} - \frac{1}{|x|}\right)\\ \lim_{x\rightarrow 0^+}\left(\frac{1}{x} - \frac{1}{|x|}\right)\\ \lim_{x\rightarrow 0}\left(\frac{1}{x} - \frac{1}{|x|}\right)$$

Find the limits using the expanded definition of limit presented in Section 1.6 . That is, limits can now include the terminology and notation of infinity . The expanded definition of limit is used in Section 1.6 Example 2 . Show all details clearly and use correct notation.
What does the result of (b) tell you about the graph of the function?

Students #7,8

Similar Problem from Exercise List: 1.6 # 19
Similar Book Example: Section 1.6 Examples 5, 11
Similar Class Example:

Find the limit of the rational function using the methods of Section 1.6 Examples 5,9 . Show all details clearly and use correct notation. $$\lim_{x\rightarrow \infty}\frac{7x^5-3x^2+13}{4x^5+199x^3-17}$$
What does the result of (a) tell you about the graph of the rational function?

Students #9,10

Similar Problem from Exercise List: 1.6 # 19
Similar Book Example: Section 1.6 Examples 5, 11
Similar Class Example:

Find the limit of the rational function using the methods of Section 1.6 Examples 5,9 . Show all details clearly and use correct notation. $$\lim_{x\rightarrow \infty}\frac{7x^5-3x^2+13}{4x^6+199x^3-17}$$
What does the result of (a) tell you about the graph of the rational function?

Students: #11,12:

Similar Problem from Exercise List: 1.6 # 19
Similar Book Example: Section 1.6 Examples 5, 11
Similar Class Example:

Find the limit of the rational function using the methods of Section 1.6 Examples 5,9 . Show all details clearly and use correct notation. $$\lim_{x\rightarrow \infty}\frac{7x^8-3x^2+13}{4x^5+199x^3-17}$$
What does the result of (a) tell you about the graph of the rational function?

Students: #13,14

Similar Problem from Exercise List: 1.6 # 25
Similar Book Example: Section 1.6 Example 6
Similar Class Example:

Find the limit of the function using the methods of Section 1.6 Example 6 . Show all details clearly and use correct notation. $$\lim_{x\rightarrow \infty} \left( \sqrt{9x^2+x}-3x\right)$$
What does the result of (a) tell you about the graph of the function?

Students: #15,16

Similar Problem from Exercise List: 1.6 # 29
Similar Book Example: Section 1.6 Examples 7,8
Similar Class Example:

Find the limit $$\lim_{x\rightarrow -\infty} \cos{(x)}$$
What does the result of (a) tell you about the graph of the function?

Students: #17,18

Similar Problem from Exercise List: 1.6 # 35
Similar Book Example:
Similar Class Example:

Find the horizontal and vertical asymptotes of the rational function. (Give their line equations and say if they are horizontal or vertical.) Explain how you determined the asymptotes. $$y=\frac{2x^2+x-1}{x^2+x-2}$$
Illustrate your results with a sketch of the graph of the function.

Students: #19,20

Similar Problem from Exercise List: 1.6 # 40
Similar Book Example:
Similar Class Example:

Find a formula for a function that has vertical asymptotes at $x=2$ and $x=5$ and horizontal asymptote $y=3$. Explain how you determined your function.
Illustrate your results with a sketch of the graph of the function that you found in (a).

Wed Sep 13: Section 2.1: Derivatives and Rates of Change ( Lecture Notes ) ( Handout on Rates of Change )

Fri Sep 15: Section 2.1: Derivatives and Rates of Change ( Lecture Notes )(Quiz Q2 ) ( Handout on Rates of Change )

Quiz Q2 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Three Problems, 10 points each, printed on front & back of one sheet of paper
- One problem based on Suggested Exercises from Section 1.5 .
- One problem based on Suggested Exercises from Section 1.6 .
- One problem based on Suggested Exercises from Section 1.6 .

Mon Sep 18: Section 2.2: The Derivative as a Function ( Lecture Notes )

Tue Sep 19: Recitation R04 : Derivatives and Rates of Change (2.1) and Calculating Derivatives (2.2)

Students Solving Problems and Discussing Their Solutions

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Sep 19 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1 and #11: Allen,Daylen
Section 101 Student #2 and #12: Bansode,Ankita
Section 101 Student #3 and #13: Bedell,Paris
Section 101 Student #4: and #14: Beegan,Caden
Section 101 Student #5 and #15: Brandt,Roman
Section 101 Student #6 and #16: Earl,Claire-Michael
Section 101 Student #7 and #17: Eisnaugle,Ethan
Section 101 Student #8 and #18: Frometa,Amelia
Section 101 Student #9 and #19: Jackson,Henry
Section 101 Student #10 and #20: Miller,Taylor and Robinson,Alana

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1 and #15: Fritz,Ronan
Section 102 Student #2 and #16: Herrmann,Mary
Section 102 Student #3 and #17: Hoffman,Sidney
Section 102 Student #4 and #18: Hubbard,Grace
Section 102 Student #5 and #19: Lavender,Kinley
Section 102 Student #6 and #20: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: Walsh,Carly
Section 102 Student #14: White,Anna

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1 and #9: Alder,Ethan
Section 103 Student #2 and #10: Blower,Carsen
Section 103 Student #3 and #11: Hains,Amanda
Section 103 Student #4 and #12: Hawley,Frank
Section 103 Student #5 and #13: Kennedy,Quinn
Section 103 Student #6 and #14: Martis,Steve
Section 103 Student #7 and #15: Mikin,Reilly
Section 103 Student #8 and #16: Winterton,Jacob
Section 103 Student #17: Unassigned Challenge Problem: Who can do it?!?
Section 103 Student #18: Unassigned Challenge Problem: Who can do it?!?
Section 103 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 103 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 104 (meets Tue 2:00pm – 2:555pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,Joseph
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned
Section 104 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 104 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Mulholland-Flint,Austin
Section 111 Student #11: Ngum,Venessa
Section 111 Student #12: Pickens,Charlee
Section 111 Student #13: Rasmussen,Cubbie
Section 111 Student #14: Rodean,Alex
Section 111 Student #15: Sahr,Griffin
Section 111 Student #16: Sautter,Jack
Section 111 Student #17: Scudder,Braedon
Section 111 Student #18: Wright,Beck
Section 111 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 111 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Lewis-Baranyai,Enzo
Section 112 Student #14: Massie,Olivia
Section 112 Student #15: Miller,Austy
Section 112 Student #16: Shields,Julia
Section 112 Student #17: Smith,Kaitlyn
Section 112 Student #18: Whittington,Kelsey
Section 112 Student #19: Williams,Ava
Section 112 Student #20: Unassigned

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Sikora,Daniella
Section 113 Student #16: Slingluff,Cheyenne
Section 113 Student #17: Wenning,Luke
Section 113 Student #18: Unassigned
Section 113 Student #19: Unassigned Challenge Problem: Who can do it?!?
Section 113 Student #20: Unassigned Challenge Problem: Who can do it?!?

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Blore,Noah
Section 114 Student #4: Cox,Madelyn
Section 114 Student #5: Dubois,Aleke
Section 114 Student #6: Elliott,Maggie
Section 114 Student #7: Hartzell,Molly
Section 114 Student #8: Kezele,Ashley
Section 114 Student #9: Lampa,Andrew
Section 114 Student #10: Mcclellan,Alex
Section 114 Student #11: Mcdermitt,Brian
Section 114 Student #12: Meyer,Morgan
Section 114 Student #13: Morris,Chase
Section 114 Student #14: Mueller,Maddy
Section 114 Student #15: Nguyen,Jim
Section 114 Student #16: Raynewater,Ty
Section 114 Student #17: Smith,Riley
Section 114 Student #18: Sobey,Lily
Section 114 Student #19: Wall,Logan
Section 114 Student #20: Young,Kiefer

The Problems to Be Done in Tue Sep 19 Recitation Meetings

Students 1,2: (2.1#16) Suppose that a function $g(x)$ is known to have these properties:

$g(5)=-3$
$g'(5)=4$

Find the equation for the line tangent to the graph of $g(x)$ at $x=5$. Start by presenting the tangent line equation in point slope form , and then convert the equation to slope intercept form . Explain how you got your result. Use a graph to illustrate.

Students 3,4: (2.1#18) Suppose that the line that is tangent to the graph of a function $f(x)$ at the point $(4,3)$ also passes through the point $(0,2)$.

Find $f(4)$
Find $f'(4)$

Explain how you got your results. Use a graph to illustrate.

Students 5,6: The graph of a function $f(x)$ can be shown by clicking on the button below. Also shown is a tangent line and a secant line, with some given points on those lines. (Notice that the graph is not drawn to scale.) Use the graph to answer the questions below. Project the graph on the screen. (If the projection system is not working, draw the graph on the whiteboard.)

What is the Average Rate of Change of $f(x)$ from $x=2$ to $x=7$ ? Explain.
What is $f'(2)$? Explain.

Students 7,8: (2.1#1) For the function $f(x)=4x-x^2$

Find the slope of the line tangent to the graph at $x=1$. Show all details clearly and explain key steps.
Remark: When finding derivatives, use the Definition of the Derivative $$f'(a)=\lim_{h\rightarrow 0} \frac{f(a+h)-f(a)}{h}$$ That is, build the limit and find its value. Show all steps clearly and explain key steps. Do not use Derivative Rules that you may have learned in previous courses.
Find the equation of the line tangent to the graph at $x=1$. Show all details clearly and explain key steps.
Sketch a graph of $f(x)$ and draw the tangent line. Label key points with their $(x,y)$ coordinates.

Students 9,10: (2.1#5) For the function $f(x)=\sqrt{x}$

Find the slope of the line tangent to the graph at $x=4$. Show all details clearly and explain key steps.
Remark: When finding derivatives, use the Definition of the Derivative $$f'(a)=\lim_{h\rightarrow 0} \frac{f(a+h)-f(a)}{h}$$ That is, build the limit and find its value. Show all steps clearly and explain key steps. Do not use Derivative Rules that you may have learned in previous courses.
Find the equation of the line tangent to the graph at $x=4$. Show all details clearly and explain key steps.
Sketch a graph of $f(x)$ and draw the tangent line. Label key points with their $(x,y)$ coordinates.

Students 11,12: (2.1#1) A ball is thrown into the air. Its height (in feet) after $t$ seconds is given by the equation $$y=40t-16t^2$$ Find the velocity when $t=2$. Show all details clearly and explain key steps.
Remark: When finding derivatives, use the Definition of the Derivative $$f'(a)=\lim_{h\rightarrow 0} \frac{f(a+h)-f(a)}{h}$$ That is, build the limit and find its value. Show all steps clearly and explain key steps. Do not use Derivative Rules that you may have learned in previous courses.

Students 13,14: (This is the messiest problem. Sorry!) (2.1#27) For the function $$f(t)=\frac{2t+1}{t+3}$$

Find $f'(2)$.
Remark: When finding derivatives, use the Definition of the Derivative $$f'(a)=\lim_{h\rightarrow 0} \frac{f(a+h)-f(a)}{h}$$ That is, build the limit and find its value. Show all steps clearly and explain key steps. Do not use Derivative Rules that you may have learned in previous courses.
What is the slope of the line tangent to the graph of $f(t)$ at $t=2$? Explain.

Students 15,16: (2.2#19) For the function $$f(x)=3x-5$$

Find $f'(x)$ using the Definition of the Derivative $$f'(x)=\lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h}$$ That is, build the limit and find its value. (Do not use Derivative Rules that you may have learned in previous courses.) Show all steps clearly and explain key steps.
What is the slope of the line tangent to the graph of $f(x)$ at $x=7$? Explain, using a graph of $f(x)$.

Students 17,18: (2.2#22) For the function $$g(t)=\frac{1}{\sqrt{t}}$$

Find $g'(t)$ using the Definition of the Derivative $$g'(t)=\lim_{h\rightarrow 0} \frac{g(t+h)-g(t)}{x}$$ That is, build the limit and find its value. (Do not use Derivative Rules that you may have learned in previous courses.) Show all steps clearly and explain key steps.
What is the slope of the line tangent to the graph of $f(x)$ at $x=9$? Explain.

Students 19,20 (2.2#23) For the function $$g(x)=\frac{1}{x}$$

Find $g'(x)$ using the Definition of the Derivative $$g'(x)=\lim_{h\rightarrow 0} \frac{g(x+h)-g(x)}{x}$$ That is, build the limit and find its value. (Do not use Derivative Rules that you may have learned in previous courses.) Show all steps clearly and explain key steps.
What is the slope of the line tangent to the graph of $g(x)$ at $x=5$? Explain.

Wed Sep 20: Section 2.2: The Derivative as a Function ( Lecture Notes from Section 100 (Isaac Agyei) ) ( Lecture Notes from Section 110 (Kenny So) )

Fri Sep 22: Exam X1 Covering Through Section 2.2

Exam X1 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
The Exam will last the full duration of the class period.
No books, notes, calculators, or phones
Eight problems, 25 points each, printed on front & back of three sheets of paper. All problems are based on suggested exercises.
1. A problem about limits, based on suggested exercises from Section 1.3
2. A problem about calculating limits, based on suggested exercises from Section 1.4
3. A problem using the concept of continuity, based on suggested exercises from Section 1.5
4. A problem about calculating a limit involving infinity, based on suggested exercises from Section 1.6
5. A problem about calculating a limit involving infinity, based on suggested exercises from Section 1.6
6. A problem about derivatives and rates of change, based on suggested exercises from Section 2.1
7. A problem about calculating a derivative, based on suggested exercises from Section 2.2
8. A problem involving a tangent line, based on suggested exercises from Sections 2.1 and 2.2

Mon Sep 25: Section 2.3: Basic Differentiation Formulas ( Lecture Notes )

Tue Sep 26: Recitation R05 : Using Basic Differentiation Formulas (Section 2.5)

Students Solving Problems and Discussing Their Solutions

Scoring: If a student (either alone or as part of a team of two students) presents a solution to their assigned problem on the white board, their R05 score will be in the range 1/5 to 5/5 (depending on whether they have prepared ahead of time). If they do not present a solution, their R05 score will be 0/5.

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Sep 26 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bansode,Ankita
Section 101 Student #3: Bedell,Paris
Section 101 Student #4: Beegan,Caden
Section 101 Student #5: Brandt,Roman
Section 101 Student #6: Earl,Claire-Michael
Section 101 Student #7: Eisnaugle,Ethan
Section 101 Student #8: Frometa,Amelia
Section 101 Student #9: Jackson,Henry
Section 101 Student #10: Miller,Taylor
Section 101 Student #11: Robinson,Alana
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,
Section 101 Student #19: Unassigned,
Section 101 Student #20: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: Walsh,Carly
Section 102 Student #14: White,Anna
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,
Section 102 Student #19: Unassigned,
Section 102 Student #20: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,
Section 103 Student #19: Unassigned,
Section 103 Student #20: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:555pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,
Section 104 Student #19: Unassigned,
Section 104 Student #20: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Mulholland-Flint,Austin
Section 111 Student #11: Ngum,Venessa
Section 111 Student #12: Pickens,Charlee
Section 111 Student #13: Rasmussen,Cubbie
Section 111 Student #14: Rodean,Alex
Section 111 Student #15: Sahr,Griffin
Section 111 Student #16: Sautter,Jack
Section 111 Student #17: Scudder,Braedon
Section 111 Student #18: Wright,Beck
Section 111 Student #19: Unassigned,
Section 111 Student #20: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Lewis-Baranyai,Enzo
Section 112 Student #14: Massie,Olivia
Section 112 Student #15: Miller,Austy
Section 112 Student #16: Unassigned,
Section 112 Student #17: Shields,Julia
Section 112 Student #18: Smith,Kaitlyn
Section 112 Student #19: Whittington,Kelsey
Section 112 Student #20: Williams,Ava

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Sikora,Daniella
Section 113 Student #16: Slingluff,Cheyenne
Section 113 Student #17: Wenning,Luke
Section 113 Student #18: Unassigned,
Section 113 Student #19: Unassigned,
Section 113 Student #20: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Blore,Noah
Section 114 Student #4: Cox,Madelyn
Section 114 Student #5: Dubois,Aleke
Section 114 Student #6: Elliott,Maggie
Section 114 Student #7: Hartzell,Molly
Section 114 Student #8: Kezele,Ashley
Section 114 Student #9: Lampa,Andrew
Section 114 Student #10: Mcclellan,Alex
Section 114 Student #11: Mcdermitt,Brian
Section 114 Student #12: Meyer,Morgan
Section 114 Student #13: Morris,Chase
Section 114 Student #14: Mueller,Maddy
Section 114 Student #15: Nguyen,Jim
Section 114 Student #16: Raynewater,Ty
Section 114 Student #17: Smith,Riley
Section 114 Student #18: Sobey,Lily
Section 114 Student #19: Wall,Logan
Section 114 Student #20: Young,Kiefer

Basic Derivative Formulas

Derivative of a Constant Function If $c$ is a constant, then $$\frac{d}{dx}(c)=0$$

The Power Rule If $n$ is any real number, then $$\frac{d}{dx}\left(x^n \right)=nx^{n-1}$$

The Sum Constant Multiple Rule If $a$ and $b$ are constants and $f$ and $g$ are differentiable functions, then $$\frac{d}{dx}\left[af(x) +bg(x)\right]=a\frac{d}{dx}f(x)+b\frac{d}{dx}g(x)$$

The Sine and Cosine Rules (Not discussed in class Monday, but simple enough.) $$\frac{d}{dx}\sin{(x)}=\cos{(x)}$$ $$\frac{d}{dx}\cos{(x)}=-\sin{(x)}$$

First Problems to Be Done in Tue Sep 26 Recitation Meetings: Derivatives

Students 1,2 (first problem)(You'll have another problem later.) (2.3#2) Find the derivative of the function $$f(x) = \pi^2$$ Show all details clearly and use correct notation.

Students 3,4 (first problem)(You'll have another problem later.) (2.3#3) Find the derivative of the function $$f(t)=2-\frac{2}{3}t$$ Show all details clearly and use correct notation.

Students 5,6 (first problem)(You'll have another problem later.) (2.3#4) For the function $F(x)=\frac{3}{4}x^8$

Find $F(2)$
Find $F'(x)$
Find $F'(2)$
Find the height of the graph of $F(x)$ at $x=2$.
Find the slope of the graph of $F(x)$ at $x=2$.

Students 7,8 (first problem)(You'll have another problem later.) (2.3#5) For the function $f(x)=x^3-4x+6$

Find $F(3)$
Find $F'(x)$
Find $F'(3)$
Find the height of the graph of $f(x)$ at $x=3$.
Find the slope of the graph of $f(x)$ at $x=3$.

Students 9,10 (first problem)(You'll have another problem later.) (2.3#7) For the function $f(x)=3x^2-2\cos{(x)}$

Find $F(\pi)$
Find $F'(x)$
Find $F'(\pi)$
Find the height of the graph of $f(x)$ at $x=\pi$. (Give an exact answer in symbols, not a decimal approximation.)
Find the slope of the graph of $f(x)$ at $x=\pi$. (Give an exact answer in symbols, not a decimal approximation.)

Students 11,12 (first problem)(You'll have another problem later.) (2.3#9) Find the derivative of the function $$g(x)=x^2(1-2x)$$ Show all details clearly and use correct notation.

Students 13,14 (first problem)(You'll have another problem later.) For the function $f(x)=2x^{1/3}$

Find $f(8)$ (no calculators!)
Find $f'(x)$
Find $f'(8)$ (no calculators!)
Find the height of the graph of $f(x)$ at $x=8$.
Find the slope of the graph of $f(x)$ at $x=8$.

Students 15,16 (first problem)(You'll have another problem later.) (2.3#11) Find the derivative of the function $$f(t)=\frac{2}{t^{3/4}}$$ Show all details clearly and use correct notation

Students 17,18 (first problem)(You'll have another problem later.) (2.3#19) For the function $$f(x)=\frac{x^2+4x+3}{\sqrt{x}}$$

Rewrite $f(x)$ in power function form . That is, write it in the form $$f(x)=ax^p+bx^q+cx^r$$ where $a,b,c,p,q,r$ are real numbers.
Find $f'(x)$

Students 19,20 (first problem)(You'll have another problem later.) (2.3#21) For the function $$v=t^2-\frac{1}{\sqrt[4]{t^3}}$$

Rewrite the function in power function form . That is, write it in the form $$v(t)=at^p+bt^q$$ where $a,b,p,q$ are real numbers.
Find $v'(t)$

Second Problems to Be Done in Tue Sep 26 Recitation Meetings: Tangent Lines and Normal Lines

Remember that the line tangent to the graph of $f(x)$ at $x=a$ is the line that has these two properties

The line touches the graph of $f(x)$ at $x=a$. So the line contains the point $(x,y)=(a,f(a))$, called the point of tangency
The line has slope $m=f'(a)$

Therefore, the tangent line has line equation (in point slope form ) $$(y-f(a))=f'(a)\cdot(x-a)$$

A new thing, the line normal to the graph of $f(x)$ at $x=a$ , is the line that has these two properties

The line touches the graph of $f(x)$ at $x=a$. So the line contains the point $(x,y)=(a,f(a))$
The line is perpendicular to the line that is tangent to the graph at that point. That is,
- If the tangent line has slope $m_T\neq 0$, then the normal line has slope $$m_N=-\frac{1}{m_T}$$
- If the tangent line has slope $m_T = 0$, which indicates that the tangent is horizontal , then the normal line is vertical .

I'll leave it to you to figure out the form of the equation of the normal line in those two cases.

Students 1- 12 (second problem) (2.3#27) For the function $$f(x)=2\sin{(x)}$$

Students 1,2: Find the equation for the line tangent to the graph of $f(x)$ at $x=\frac{\pi}{3}$ . Draw the graph and draw your tangent line. Label important stuff.
Students 3,4: Find the equation for the line normal to the graph of $f(x)$ at $x=\frac{\pi}{3}$ . Draw the graph and draw your normal line. Label important stuff.
Students 5,6: Find the equation for the line tangent to the graph of $f(x)$ at $x=\frac{\pi}{2}$ . Draw the graph and draw your tangent line. Label important stuff.
Students 7,8: Find the equation for the line normal to the graph of $f(x)$ at $x=\frac{\pi}{2}$ . Draw the graph and draw your normal line. Label important stuff.
Students 9,10: Find the equation for the line tangent to the graph of $f(x)$ at $x=\frac{3\pi}{4}$ . Draw the graph and draw your tangent line. Label important stuff.

Students 11 - 20 (second problem) (2.3#29) For the function $$f(x)=-x^2+8x=-x(x-8)$$

Students 11,12: Find the equation for the line tangent to the graph of $f(x)$ at $x=2$ . Draw the graph and draw your tangent line. Label important stuff.
Students 13,14: Find the equation for the line normal to the graph of $f(x)$ at $x=2$ . Draw the graph and draw your normal line. Label important stuff.
Students 15,16: Find the equation for the line tangent to the graph of $f(x)$ at $x=4$ . Draw the graph and draw your tangent line. Label important stuff.
Students 17,18: Find the equation for the line normal to the graph of $f(x)$ at $x=4$ . Draw the graph and draw your normal line. Label important stuff.
Students 19,20: Find the equation for the line tangent to the graph of $f(x)$ at $x=5$ . Draw the graph and draw your tangent line. Label important stuff.

Wed Sep 27: Section 2.3: Basic Differentiation Formulas ( Lecture Notes ) ( Class Drill on Rewriting Function Before Differentiating )

Fri Sep 29: Section 2.4: The Product and Quotient Rules ( Lecture Notes )(Quiz Q3 )

Quiz Q3 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Three Problems, 10 points each, about using the Basic Differentiation Formulas, based on Suggested Exercises from Section 2.3, printed on front & back of one sheet of paper.

Mon Oct 2: Section 2.5: The Chain Rule ( Lecture Notes )

Tue Oct 3: Recitation R06 : Using Differentiation Formulas (Sections 2.3, 2.4, 2.5)

Student Numbers for Tue Oct 3 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bansode,Ankita
Section 101 Student #3: Bedell,Paris
Section 101 Student #4: Beegan,Caden
Section 101 Student #5: Brandt,Roman
Section 101 Student #6: Earl,Claire-Michael
Section 101 Student #7: Eisnaugle,Ethan
Section 101 Student #8: Frometa,Amelia
Section 101 Student #9: Jackson,Henry
Section 101 Student #10: Miller,Taylor
Section 101 Student #11: Robinson,Alana
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,
Section 101 Student #19: Unassigned,
Section 101 Student #20: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: Walsh,Carly
Section 102 Student #14: White,Anna
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,
Section 102 Student #19: Unassigned,
Section 102 Student #20: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,
Section 103 Student #19: Unassigned,
Section 103 Student #20: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:555pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,
Section 104 Student #19: Unassigned,
Section 104 Student #20: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Mulholland-Flint,Austin
Section 111 Student #11: Ngum,Venessa
Section 111 Student #12: Pickens,Charlee
Section 111 Student #13: Rasmussen,Cubbie
Section 111 Student #14: Rodean,Alex
Section 111 Student #15: Sahr,Griffin
Section 111 Student #16: Sautter,Jack
Section 111 Student #17: Scudder,Braedon
Section 111 Student #18: Wright,Beck
Section 111 Student #19: Unassigned,
Section 111 Student #20: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Lewis-Baranyai,Enzo
Section 112 Student #14: Massie,Olivia
Section 112 Student #15: Miller,Austy
Section 112 Student #16: Unassigned,
Section 112 Student #17: Shields,Julia
Section 112 Student #18: Smith,Kaitlyn
Section 112 Student #19: Whittington,Kelsey
Section 112 Student #20: Williams,Ava

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Sikora,Daniella
Section 113 Student #16: Slingluff,Cheyenne
Section 113 Student #17: Wenning,Luke
Section 113 Student #18: Unassigned,
Section 113 Student #19: Unassigned,
Section 113 Student #20: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Blore,Noah
Section 114 Student #4: Cox,Madelyn
Section 114 Student #5: Dubois,Aleke
Section 114 Student #6: Elliott,Maggie
Section 114 Student #7: Hartzell,Molly
Section 114 Student #8: Kezele,Ashley
Section 114 Student #9: Lampa,Andrew
Section 114 Student #10: Mcclellan,Alex
Section 114 Student #11: Mcdermitt,Brian
Section 114 Student #12: Meyer,Morgan
Section 114 Student #13: Morris,Chase
Section 114 Student #14: Mueller,Maddy
Section 114 Student #15: Nguyen,Jim
Section 114 Student #16: Raynewater,Ty
Section 114 Student #17: Smith,Riley
Section 114 Student #18: Sobey,Lily
Section 114 Student #19: Wall,Logan
Section 114 Student #20: Young,Kiefer

Basic Derivative Formulas

Derivative of a Constant Function If $c$ is a constant, then $$\frac{d}{dx}(c)=0$$

The Power Rule If $n$ is any real number, then $$\frac{d}{dx}\left(x^n \right)=nx^{n-1}$$

The Product Rule $$\frac{d}{dx}\left(\text{left}(x) \cdot \text{right}(x)\right)=\left(\frac{d}{dx}\text{left}(x)\right) \cdot \text{right}(x)+\text{left}(x) \cdot \left(\frac{d}{dx}\text{right}(x)\right)$$

The Quotient Rule $$\frac{d}{dx}\left(\frac{\text{top}(x)}{\text{bottom}(x)}\right)=\frac{\left(\frac{d}{dx}\text{top}(x)\right) \cdot \text{bottom}(x)-\text{top}(x) \cdot \left(\frac{d}{dx}\text{bottom}(x)\right)}{(\text{bottom}(x))^2}$$

The Chain Rule $$\frac{d}{dx}\text{outer}(\text{inner}(x))=\text{outer}'(\text{inner}(x))\cdot\text{inner}'(x)$$

Derivatives of Trig Functions $$\frac{d}{dx}\sin{(x)}=\cos{(x)}$$ $$\frac{d}{dx}\cos{(x)}=-\sin{(x)}$$ $$\frac{d}{dx}\tan(x)=(\sec(x))^2$$ $$\frac{d}{dx}\csc{(x)}=-\csc{(x)}\cot{(x)}$$ $$\frac{d}{dx}\sec{(x)}=\sec{(x)}\tan{(x)}$$ $$\frac{d}{dx}\cot{(x)}=-(\csc(x))^2$$

Part 1: Students Solving Problems and Discussing Their Solutions

Scoring: If a student (either alone or as part of a team of two students) presents a solution to their assigned problem on the white board, their R06 score will be in the range 1/5 to 5/5 (depending on whether they have prepared ahead of time). If they do not present a solution, their R07 score will be 0/5.

Students 1,2 (2.4#3) Find the derivative of the function $$g(t)=t^4\cos{(t)}$$ Show all details clearly and use correct notation.

Students 3,4 (2.4#13) Find the derivative of the function $$f(x)=\frac{x^3}{5-x^2}$$ Show all details clearly and use correct notation.

Students 5,6 (2.4#16) Find the derivative of the function $$g(t)=\frac{t-\sqrt{t}}{t^{2/3}}$$ Show all details clearly and use correct notation. Hint: The function is presented as a quotient , but the derivative is very hard if you use the Quotient Rule . Simplify the function by first rewriting it in power function form , and then finding the derivative using simpler rules .

Students 7,8 (2.4#17) Find the derivative of the function $$f(t)=\frac{5t}{5+\sqrt{t}}$$ Show all details clearly and use correct notation.

Students 9,10 (2.4#19) Find the derivative of the function $$f(x)=\frac{x}{3-\tan{(x)}}$$ Show all details clearly and use correct notation.

Students 11,12 (2.4#27) Find the equation of the line tangent to the graph of $$f(x)=\frac{x^2-1}{x^2+x+1}$$ at $x=1$. Present your line equation in slope intercept form . Show all details clearly and use correct notation.

Students 13,14 (2.4#31) Find the equation of the line tangent to the graph of $$f(x)=\frac{1}{1+x^2}$$ at $x=-1$. Present your line equation in slope intercept form . Show all details clearly and use correct notation.

Students 15,16 (2.5#1) Find the derivative of $$f(x)=\sqrt[3]{1+4x}$$ Show all details clearly and use correct notation.

Students 17,18 (2.5#13) Find the derivative of $$f(x)=\cos{(a^3+x^3)}$$ Show all details clearly and use correct notation.

Students 19,20 (2.5#51) Find the $(x,y)$ coordinates of all points on the graph of $$f(x)=2\sin{(x)}+\sin^2{(x)}$$ that have horizontal tangent lines. Show all details clearly and use correct notation.

Part 2: Conceptual Questions about Tangent Lines

Instructor Ask Question #1 for the Class: Frick and Frack have been asked the following:

Find the slope of the line tangent to the graph of $f(x)=x^3$ at $x=5$.

They are arguing about the result.

Frick says that the slope is $ 3x^2 $ because the derivative is the tangent line .
Frack that the the slope is $$ m=\frac{f(6)-f(5)}{6-5}=\frac{216-125}{1}=91$$

Who is right? Explain.

Frick and Frack are both wrong!

Frick says that the derivative is the tangent line. But this is not correct. The objective is to find the slope of the tangent line . This will be a number . The derivative is a function , not a number . (The derivative is a function that can be used to find the number that is the slope of the tangent line .)

Frack is also wrong. Frack computed the slope of a secant line .

The correct procedure to find the slope of the line tangent to the graph of $f(x)=x^3$ at $x=5$ is as follows.

Step 1: Find $f'(x)$. The result is

$$ \frac{d}{dx}x^3=3x^{3-1}=3x^2$$

Step 2: Substitute $x=5$ into $f'(x)$ to get $m=f'(5)$. The result is

$$ m=f'(5)=3(5)^2=3\cdot25=75$$

Instructor Ask Question #2 for the Class: Wacky Jack has been asked the following:

Find the equation of the line tangent to the graph of some function $g(x)$ at $x=7$.

Their answer was $$y=2x^3-5x^2+4x-11$$ Which of these three statements is true?

Wacky Jack's answer is correct.
Wacky Jack's answer is incorrect.
There is not enough information to be able to say whether Wacky Jack's answer is correct or incorrect. One needs to know the function $g(x)$ in order to judge.

At first, you might think that of course one would need more information before being able to say whether Wacky Jack's answer is correct or incorrect. But in fact, it is easy to see immediately that Wacky Jack's answer is incorrect .

The key is to remember that Wacky Jack was asked to find the equation of a line . That means that their result must be in the form $$y=mx+b$$ where $m$ and $b$ are numbers . Since Wacky Jack's answer is not in that form, their answer is incorrect.

This example illustrates one kind of quick check on problems involving finding the equation of a tangent line. You will encounter problems of that sort where the calculations get quite messy. But the end result should always be an equation of the form $y=mx+b$.

Instructor Ask Question #3 for the Class: For the function

$$f(x)=5x^3-7x^2+11x-13$$ find the following:

the $y$ intercept of $f(x)$
the $y$ intercept of $f'(x)$
the $y$ intercept of the the line tangent to $f(x)$ at $x=2$

Take-away from this exercise: Observe that these three $y$ intercepts are three different things. In tangent line problems, a few of you mistakenly use the $y$ intercept of $f(x)$, or the $y$ intercept of $f'(x)$, as $y$ intercept of the the line tangent to $f(x)$ at $x=a$.

Wed Oct 4: Section 2.6: Implicit Differentiation ( Lecture Notes )

Fri Oct 6: Section 2.7: Related Rates ( Lecture Notes ) ( Handout on Implicit Differentiation and related Rates ) (Quiz Q4 )

Quiz Q4 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
four Problems, printed on front & back of one sheet of paper
- One Product Rule problem based on Suggested Exercises from Section 2.4 .
- One Quotient Rule problem based on Suggested Exercises from Section 2.4 .
- One Chain Rule problem based on Suggested Exercises from Section 2.5 .
- One Implicit Differentiation problem based on Suggested Exercises from Section 2.6 .

Mon Oct 9: Section 2.8: Linear Approx & Differentials ( Lecture Notes ) ( Handout on Linearizations and the Method of Using a Linear Approximation )

Tue Oct 10: Recitation R07 : Related Rates and Linearizations (Sections 2.7 and 2.8)

Student Numbers for Tue Oct 10 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bansode,Ankita
Section 101 Student #3: Bedell,Paris
Section 101 Student #4: Beegan,Caden
Section 101 Student #5: Brandt,Roman
Section 101 Student #6: Earl,Claire-Michael
Section 101 Student #7: Eisnaugle,Ethan
Section 101 Student #8: Frometa,Amelia
Section 101 Student #9: Jackson,Henry
Section 101 Student #10: Miller,Taylor
Section 101 Student #11: Robinson,Alana
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,
Section 101 Student #19: Unassigned,
Section 101 Student #20: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: Walsh,Carly
Section 102 Student #14: White,Anna
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,
Section 102 Student #19: Unassigned,
Section 102 Student #20: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,
Section 103 Student #19: Unassigned,
Section 103 Student #20: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:555pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,
Section 104 Student #19: Unassigned,
Section 104 Student #20: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Mulholland-Flint,Austin
Section 111 Student #11: Ngum,Venessa
Section 111 Student #12: Pickens,Charlee
Section 111 Student #13: Rasmussen,Cubbie
Section 111 Student #14: Rodean,Alex
Section 111 Student #15: Sahr,Griffin
Section 111 Student #16: Sautter,Jack
Section 111 Student #17: Scudder,Braedon
Section 111 Student #18: Wright,Beck
Section 111 Student #19: Unassigned,
Section 111 Student #20: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Lewis-Baranyai,Enzo
Section 112 Student #14: Massie,Olivia
Section 112 Student #15: Miller,Austy
Section 112 Student #16: Unassigned,
Section 112 Student #17: Shields,Julia
Section 112 Student #18: Smith,Kaitlyn
Section 112 Student #19: Whittington,Kelsey
Section 112 Student #20: Williams,Ava

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Sikora,Daniella
Section 113 Student #16: Slingluff,Cheyenne
Section 113 Student #17: Wenning,Luke
Section 113 Student #18: Unassigned,
Section 113 Student #19: Unassigned,
Section 113 Student #20: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Blore,Noah
Section 114 Student #4: Cox,Madelyn
Section 114 Student #5: Dubois,Aleke
Section 114 Student #6: Elliott,Maggie
Section 114 Student #7: Hartzell,Molly
Section 114 Student #8: Kezele,Ashley
Section 114 Student #9: Lampa,Andrew
Section 114 Student #10: Mcclellan,Alex
Section 114 Student #11: Mcdermitt,Brian
Section 114 Student #12: Meyer,Morgan
Section 114 Student #13: Morris,Chase
Section 114 Student #14: Mueller,Maddy
Section 114 Student #15: Nguyen,Jim
Section 114 Student #16: Raynewater,Ty
Section 114 Student #17: Smith,Riley
Section 114 Student #18: Sobey,Lily
Section 114 Student #19: Wall,Logan
Section 114 Student #20: Young,Kiefer

Basic Derivative Formulas

Derivative of a Constant Function If $c$ is a constant, then $$\frac{d}{dx}(c)=0$$

The Power Rule If $n$ is any real number, then $$\frac{d}{dx}\left(x^n \right)=nx^{n-1}$$

The Chain Rule $$\frac{d}{dx}\text{outer}(\text{inner}(x))=\text{outer}'(\text{inner}(x))\cdot\text{inner}'(x)$$

Students Solving Problems and Discussing Their Solutions

Each student will solve two problems: One problem in Round 1 , and another problem in Round 2 .

Problems for Oct 10 Round 1

Students 1,2 (2.7#4) The length of a rectangle is increasing at a rate of $8$ cm/s and its width is increasing at a rate of $3$ cm/s. When the length is $20$ cm and the width is $10$ cm, how fast is the area of the rectangle increasing? Make a good drawing and use correct units in your answer.

Students 3,4 (2.7#5) A cylindrical tank with radius $5$m is being filled with water at a rate of $3$ m ³ /min. How fast is the height of the water increasing? Make a good drawing and use correct units in your answer.

Hint: Make sure that you start with the correct equation describing the relationship between the radius, height, and volume of a cylinder! Look it up to make sure that you have it right.

Students 5,6 (2.7#11) A snowball melts so that its surface area decreases at a rate of $1$ cm ³ /min. Find the rate at which the diameter decreases when the diameter is $10$ cm. Make a good drawing and use correct units in your answer.

Hint: You'll have to start by coming up with an equation describing the relationship between the surface area of a sphere and diameter of the sphere . If you look up the equation for the surface area of a sphere, you'll probably find an equation that relates the surface area to the radius . Convert that equation to a new equation that relates the surface area to the diameter .

Students 7,8 (2.7#13) A plane flying horizontally at an altitude of $1$ mi and a speed of $500$ mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is $2$ mi away from the station. Make a good drawing and use correct units in your answer. (Observe that this problem is not clearly written. The phrase distance from the plane to the station refers to the length of the hypotenuse of the triangle .)

Hint: Make a right triangle with base $b$, height $h$, and hypotenuse $L$. Identify the given information in terms of $b$, $h$, and $L$. Observe that you are being asked to find $L'$. Use the Pythagorean Theorem to get an equation that expresses a relationship between $b$, $h$, and $L$. Then use Implicit Differentiation to get a new equation that expresses a relationship between $b,h,L,b�,h�,L'$. Solve this equation for $L'$. Then plug in known values to get a value for $L'$.

Students 9,10 (2.7#15) Two cars start moving from the same point. One travels south at $60$ mi/h and the other travels west at $25$ mi/h. At what rate is the distance between the cars increasing two hours later? Make a good drawing and use correct units in your answer.

Hint: Make a right triangle with base $b$, height $h$, and hypotenuse $L$. Identify the given information in terms of $b$, $h$, and $L$. Observe that you are being asked to find $h'$. Use the Pythagorean Theorem to get an equation that expresses a relationship between $b$, $h$, and $L$. Then use Implicit Differentiation to get a new equation that expresses a relationship between $b,h,L,b�,h�,L'$. Solve this equation for $L'$. Then plug in known values to get a value for $L'$.

Students 11,12 (2.7#25) A trough is $10$ ft long and its ends have the shape of isosceles triangles that are $3$ ft across the top and have a height of $1$ ft. The trough is being filled with water at a rate of $12$ ft ³ /min. How fast is the water level rising when the water is 6 inches deep? Make a good drawing and use correct units in your answer.

Hint: Notice that the problem statement uses a mixture of units for length: feet and inches . This is stupid, but it is done on purpose: You will usually have to deal with inconvenient units when you encounter math problems any real situation. My advice is: convert everything to one unit of length, either feet or inches , and work the problem that unit.

Students 13,14 (2.7#27) Gravel is being dumped from a conveyor belt at a rate of $30$ ft ³ /min, forming a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is $10$ ft high? Make a good drawing and use correct units in your answer.

Hint: A similar problem was an example in a recent Lecture .

Students 15,16 (2.7#28) A kite $100$ ft above the ground moves horizontally at a speed of $8$ ft/s. At what rate is the angle between the string and the horizontal decreasing when $200$ ft of string have been let out? (angles in radians) Make a good drawing and use correct units in your answer.

Hint: Make a right triangle with base $b$, height $h$, and hypotenuse $L$, and important angle $theta$. Identify the given information in terms of $b,h,L$. Observe that you are being asked to find $\theta'$. Find a Trig Formula to get an equation that expresses a relationship between $b$, $h$, and $\theta$. Then use Implicit Differentiation to get a new equation that expresses a relationship between $b,h,\theta,b',h',\theta'$. Solve this equation for $\theta'$. Then plug in known values to get a value for $\theta'$.

Students 17,18 A ladder $10$ ft long is leaning against a vertical wall. The foot of the ladder is sliding away from the wall a rate of $2$ ft/s. How fast is the top of the ladder sliding down the wall at the instant when the foot of the ladder is $6$ ft from the wall? Make a good drawing and use correct units in your answer.

Hint: Make a right triangle with base $b$, height $h$, and hypotenuse $L$. Identify the given information in terms of $b$, $h$, and $L$. Observe that you are being asked to find $h'$. Use the Pythagorean Theorem to get an equation that expresses a relationship between $b$, $h$, and $L$. Then use Implicit Differentiation to get a new equation that expresses a relationship between $b,h,L,b�,h�,L'$. Solve this equation for $h'$. Then plug in known values to get a value for $h'$.

Students 19,20 (2.7#31) A ladder is leaning against a vertical wall. The top of a ladder slides down the wall at a rate of $0.15$ m/s. At the moment when the ladder is $3$ m from the wall, it slides away from the wall at a rate of $0.2$ m/s. How long is the ladder? Make a good drawing and use correct units in your answer.

Hint: Make a right triangle with base $b$, height $h$, and hypotenuse $L$. Identify the given information in terms of $b,h,L$. Observe that you are being asked to find $L$. But it will be simpler to first find a value for the height $h$. Use the Pythagorean Theorem to get an equation that expresses a relationship between $b,h,L$. Then use Implicit Differentiation to get a new equation that expresses a relationship between $b,h,L,b�,h�,L'$. Solve this equation for $h$. Then plug in known values to get a value for $h$. Finally, use the stuff that you know to find a value for $L$.

Problems for Oct 10 Round 2

Students 1,2 (Similar to Exercise 2.8#5) The goal is to use a Linear Approximation to estimate the number $\sqrt{15.9}$. Answer questions (a) - (f) below.

Students 3,4 (Similar to Exercise 2.8#5) The goal is to use a Linear Approximation to estimate the number $\sqrt{16.1}$. Answer questions (a) - (f) below.

Students 5,6 (Similar to Exercise 2.8#11) The goal is to use a Linear Approximation to estimate the number $2.9^4$. Answer questions (a) - (f) below.

Students 7,8 (Similar to Exercise 2.8#11) The goal is to use a Linear Approximation to estimate the number $3.1^4$. Answer questions (a) - (f) below.

Students 9,10 (Similar to Exercise 2.8#13) The goal is to use a Linear Approximation to estimate the number $7.9^{2/3}$. Answer questions (a) - (f) below.

Students 11,12 (Similar to Exercise 2.8#13) The goal is to use a Linear Approximation to estimate the number $8.1^{2/3}$. Answer questions (a) - (f) below.

Students 13,14 (Similar to Exercise 2.8#17) The goal is to use a Linear Approximation to estimate the number $\sin(-0.1)$. (angles in radians) Answer questions (a) - (f) below.

Students 15,16 (Similar to Exercise 2.8#17) The goal is to use a Linear Approximation to estimate the number $\sin(0.1)$. (angles in radians) Answer questions (a) - (f) below.

Students 17,18 (Similar to Exercise 2.8#17) The goal is to use a Linear Approximation to estimate the number $\cos(-0.1)$. (angles in radians) Answer questions (a) - (f) below.

Students 19,20 (Similar to Exercise 2.8#17) The goal is to use a Linear Approximation to estimate the number $\cos(0.1)$. (angles in radians) Answer questions (a) - (f) below.

What is the related function , $f(x)$?
What is the inconvenient $x$ value , $\hat{x}$?
What is a convenient nearby $x$ value , $a$?
Build the Linearization of $f$ at $a$ . That is, build the function $$L(x)=f(a)+f�(a)\cdot(x-a)$$

Use your linearization to find $L(\hat{x})$. That is, find the value $$L(\hat{x})=f(a)+f�(a)\cdot(\hat{x}-a)$$ This is the estimate that was the goal of the problem.
While it might not be possible to write an exact value for $f(\hat{x})$, you can use a calculator to get a very precise (but not exact) decimal value for $f(\hat{x})$. Do that, and see how it compares to your estimate from part (e).

Wed Oct 11: Exponential Functions, Inverse Functions, Logarithms (Sections 3.1, 3.2) ( Lecture Notes )(Quiz Q5 )

Quiz Q5 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Two Problems, 15 points each, printed on front & back of one sheet of paper
- One Related Rates problem based on Suggested Exercises from Section 2.7 .
- One Linearization problem problem based on Suggested Exercises from Section 2.8 .

Fri Oct 13: Holiday

Mon Oct 16: Section 3.3: Derivatives of Logarithmic and Exponential Functions ( Lecture Notes )

Tue Oct 17: Recitation R08 : Derivatives of Logarithmic and Exponential Functions (Section 3.3)

Students Solving Problems and Discussing Their Solutions

Scoring: If a student (either alone or as part of a team of two students) presents a solution to their assigned problem on the white board, their R07 score will be in the range 1/5 to 5/5 (depending on whether they have prepared ahead of time). If they do not present a solution, their R07 score will be 0/5.

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Oct 17 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bedell,Paris
Section 101 Student #3: Beegan,Caden
Section 101 Student #4: Brandt,Roman
Section 101 Student #5: Earl,Claire-Michael
Section 101 Student #6: Eisnaugle,Ethan
Section 101 Student #7: Frometa,Amelia
Section 101 Student #8: Jackson,Henry
Section 101 Student #9: Miller,Taylor
Section 101 Student #10: Robinson,Alana
Section 101 Student #11: Unassigned,
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,
Section 101 Student #19: Unassigned,
Section 101 Student #20: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: White,Anna
Section 102 Student #14: Unassigned,
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,
Section 102 Student #19: Unassigned,
Section 102 Student #20: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,
Section 103 Student #19: Unassigned,
Section 103 Student #20: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:55pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,
Section 104 Student #19: Unassigned,
Section 104 Student #20: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Ngum,Venessa
Section 111 Student #11: Pickens,Charlee
Section 111 Student #12: Rasmussen,Cubbie
Section 111 Student #13: Rodean,Alex
Section 111 Student #14: Sahr,Griffin
Section 111 Student #15: Sautter,Jack
Section 111 Student #16: Scudder,Braedon
Section 111 Student #17: Wright,Beck
Section 111 Student #18: Unassigned,
Section 111 Student #19: Unassigned,
Section 111 Student #20: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Massie,Olivia
Section 112 Student #14: Miller,Austy
Section 112 Student #15: Shields,Julia
Section 112 Student #16: Smith,Kaitlyn
Section 112 Student #17: Williams,Ava
Section 112 Student #18: Unassigned,
Section 112 Student #19: Unassigned,
Section 112 Student #20: Unassigned,

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Slingluff,Cheyenne
Section 113 Student #16: Wenning,Luke
Section 113 Student #17: Unassigned,
Section 113 Student #18: Unassigned,
Section 113 Student #19: Unassigned,
Section 113 Student #20: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Dubois,Aleke
Section 114 Student #4: Elliott,Maggie
Section 114 Student #5: Hartzell,Molly
Section 114 Student #6: Kezele,Ashley
Section 114 Student #7: Lampa,Andrew
Section 114 Student #8: Mcclellan,Alex
Section 114 Student #9: Mcdermitt,Brian
Section 114 Student #10: Meyer,Morgan
Section 114 Student #11: Morris,Chase
Section 114 Student #12: Mueller,Maddy
Section 114 Student #13: Nguyen,Jim
Section 114 Student #14: Raynewater,Ty
Section 114 Student #15: Smith,Riley
Section 114 Student #16: Sobey,Lily
Section 114 Student #17: Wall,Logan
Section 114 Student #18: Young,Kiefer
Section 114 Student #19: Unassigned,
Section 114 Student #20: Unassigned,

Derivative Formulas That We Know So Far

Derivative of a Constant Function If $c$ is a constant, then $$\frac{d}{dx}(c)=0$$

The Power Rule If $n$ is any real number, then $$\frac{d}{dx}\left(x^n \right)=nx^{n-1}$$

The Chain Rule $$\frac{d}{dx}\text{outer}(\text{inner}(x))=\text{outer}'(\text{inner}(x))\cdot\text{inner}'(x)$$

Derivatives of Logarithmic Functions $$\frac{d}{dx}\ln{(x)}=\frac{1}{x}\text{ restricted to the domain }x\gt 0$$ $$\frac{d}{dx}\log_b{(x)}=\frac{1}{x\ln{(b)}}\text{ restricted to the domain }x\gt 0$$ $$\frac{d}{dx}\ln{(|x|)}=\frac{1}{x}$$

Derivatives of Exponential Functions $$\frac{d}{dx}e^{(x)}=e^{(x)}$$ $$\frac{d}{dx}b^{(x)}=b^{(x)}\ln{(b)}$$

Each student will solve two problems.

Round 1

Students 1,2 (3.3#1) Differentiate the function. $$f(x)=\log_{10}\left(x^3+5x^2+7x+11\right)$$

Students 3,4 (3.3#3) Differentiate the function. $$f(x)=\sin\left(\ln{(x)}\right)$$

Students 5,6 (3.3#4) Differentiate the function. $$f(x)=\ln\left(\sin^2{(x)}\right)$$

Students 7,8 (3.3#6) Differentiate the function. $$y=\frac{1}{\ln{(x)}}$$

Students 9,10 (3.3#9) Differentiate the function. $$g(x)=\ln\left(\frac{a-x}{a+x}\right)$$ Hint: This looks like a problem that would involve three rules: The Chain Rule (to deal with the nested function), the Logarithm Rule (to deal with the derivative of the outer function), and the Quotient Rule (to deal with the derivative of the innner function). While the problem can be done that way, there is a way to make the derivative much simpler. Before taking the derivative, use a rule of logarithms to rewrite the function $g(x)$ so that it is not the logarithm of a quotient. Then find the derivative of the rewritten function.

Students 11,12 (3.3#13) Differentiate the function. $$G(x)=\ln\left(\frac{(2x+1)^5}{\sqrt{x^2+1}}\right)$$ Hint: This looks like a problem that would involve many rules: The Chain Rule (to deal with the nested function), the Logarithm Rule (to deal with the derivative of the outer function), the Quotient Rule and Chain Rule (again!) (to deal with the derivative of the innner function). While the problem can be done that way, there is a way to make the derivative much simpler. Before taking the derivative, use a rule of logarithms to rewrite the function $G(x)$ so that it is not the logarithm of a quotient and then use another rule of logarithms to rewrite $G(x)$ so that the inside functions are simple polynomials, not nested functions. Then find the derivative of the rewritten $G(x)$.

Students 13,14 (3.3#20) Differentiate the function. $$g(x)=\sqrt{x}e^{(x)}$$

Students 15,16 (3.3#26) Differentiate the function. $$y=10^\left(1-x^2\right)$$

Students 17,18 (3.3#31) Differentiate the function. $$f(t)=\tan{\left(e^{(t)}\right)}+e^{\tan{(t)}}$$

Students 19,20 (3.3#35) Differentiate the function. $$y=2x\log_{10}{\left(\sqrt{x}\right)}$$ Hint: This looks like a problem that would involve many rules: The Product Rule (to deal with the product), the Logarithm base $b$ Rule (to deal with the $\log_b$), the Chain Rule (to deal with the nested function), and the Power Rule (to deal with the square root). While the problem can be done that way, there is a way to make the derivative much simpler. Before taking the derivative, use a rule of logarithms to rewrite the function so that it is not the logarithm of a square root. Then find the derivative of the rewritten function.

Round 2

Students 1,2,3,4 (3.3#41) Find $y'$ and $y''$ $$y=e^{(\alpha x)}\sin{(\beta x)}$$

Students 5,6,7,8 (3.3#45) Find the equation of the line tangent to the graph of $y=\ln{\left(x^2-4x+5\right)}$ at $x=3$.

Students 9,10,11,12 For the function $f(x)=e^{\left(-x^2+2x-1\right)}$

Find $f'(x)$.
Find the slope of the line tangent to the graph of $f(x)$ at $x=0$.
Find the $x$ coordinates of all points on the graph of $f(x)$ that have horizontal tangent lines .
Illustrate your results from (b),(c) using a graph of $f(x)$. Feel free to get a graph from Desmos. What famous shape is this graph?

Students 13,14,15,16 (3.3#55) Use logarithmic differentiation to find the derivative. $$y=x^x$$

Students 17,18,19,20 (3.3#57) Use logarithmic differentiation to find the derivative. $$y=\left(\cos{(x)}\right)^x$$

Wed Oct 18: Section 3.4: Exponential Growth & Decay ( Lecture Notes )

Fri Oct 20: Exam X2 Covering Section 2.3 through Chapter 3

Exam X2 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
The Exam will last the full duration of the class period.
No books, notes, calculators, or phones
Eight problems, 25 points each, printed on front & back of three sheets of paper. All problems are based on suggested exercises.
- Four problems about finding derivatives using various methods that we have studied (in sections 2.3, 2.4, 2.5, 2.6, 3.3)
- Four problems about using derivatives to find things.
  - Related rates (Section 2.7)
  - Exponential Growth in Biology or Exponential Decay of Radioactive Substance (Section 3.4)
  - Velocity & Acceleration (Problems about this appear in Sections 2.3, 2.4, 2.5.)
  - Slope or Equation of the Tangent Line and/or Normal Line. (Problems about this appear in Sections 2.3, 2.4, 2.5, 3.3.)

Mon Oct 23: Section 4.1: Maximum and Minimum Values ( Lecture Notes )

Tue Oct 24: Recitation R09 : Extrema and Critical Numbers (Section 4.1)

Students Solving Problems and Discussing Their Solutions

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Oct 24 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bedell,Paris
Section 101 Student #3: Beegan,Caden
Section 101 Student #4: Brandt,Roman
Section 101 Student #5: Earl,Claire-Michael
Section 101 Student #6: Eisnaugle,Ethan
Section 101 Student #7: Jackson,Henry
Section 101 Student #8: Miller,Taylor
Section 101 Student #9: Robinson,Alana
Section 101 Student #10: Unassigned,
Section 101 Student #11: Unassigned,
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,
Section 101 Student #19: Unassigned,
Section 101 Student #20: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: White,Anna
Section 102 Student #14: Unassigned,
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,
Section 102 Student #19: Unassigned,
Section 102 Student #20: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,
Section 103 Student #19: Unassigned,
Section 103 Student #20: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:55pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,
Section 104 Student #19: Unassigned,
Section 104 Student #20: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Mckinney,Kaia
Section 111 Student #10: Ngum,Venessa
Section 111 Student #11: Pickens,Charlee
Section 111 Student #12: Rasmussen,Cubbie
Section 111 Student #13: Rodean,Alex
Section 111 Student #14: Sahr,Griffin
Section 111 Student #15: Sautter,Jack
Section 111 Student #16: Scudder,Braedon
Section 111 Student #17: Wright,Beck
Section 111 Student #18: Unassigned,
Section 111 Student #19: Unassigned,
Section 111 Student #20: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Massie,Olivia
Section 112 Student #14: Miller,Austy
Section 112 Student #15: Shields,Julia
Section 112 Student #16: Smith,Kaitlyn
Section 112 Student #17: Williams,Ava
Section 112 Student #18: Unassigned,
Section 112 Student #19: Unassigned,
Section 112 Student #20: Unassigned,

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Slingluff,Cheyenne
Section 113 Student #16: Wenning,Luke
Section 113 Student #17: Unassigned,
Section 113 Student #18: Unassigned,
Section 113 Student #19: Unassigned,
Section 113 Student #20: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Dubois,Aleke
Section 114 Student #4: Elliott,Maggie
Section 114 Student #5: Hartzell,Molly
Section 114 Student #6: Kezele,Ashley
Section 114 Student #7: Lampa,Andrew
Section 114 Student #8: Mcclellan,Alex
Section 114 Student #9: Mcdermitt,Brian
Section 114 Student #10: Meyer,Morgan
Section 114 Student #11: Morris,Chase
Section 114 Student #12: Mueller,Maddy
Section 114 Student #13: Nguyen,Jim
Section 114 Student #14: Raynewater,Ty
Section 114 Student #15: Smith,Riley
Section 114 Student #16: Sobey,Lily
Section 114 Student #17: Wall,Logan
Section 114 Student #18: Young,Kiefer
Section 114 Student #19: Unassigned,
Section 114 Student #20: Unassigned,

Recitation Part 1: Finding Critical Numbers of Functions

Remember the definition of Critical Number from the Monday March 20 Lecture. (The wording of Barsamian's definition differs from the wording of the book's definition, but the underlying meaning is the same.)

Definition: A Critical Number of a function $f(x)$ is an $x=c$ that satisfies both of these requirements:

$f(c)$ exists. (That is, $x=c$ is in the domain of $f(x)$.
$f'(c)=0$ or $f'(c)$ does not exist .

Each student will answer questions related to finding the critical numbers of a function.

For each function $f(x)$, answer the following questions:

Find the domain of $f(x)$.
Find $f'(x)$.
Find the domain of $f'(x)$.
Find all $x$ values that are in the domain of $f(x)$ but that are not in the domain of $f'(x)$. That is, find all $x$ values such that $f(x)$ exists but $f'(x)$ does not exist. Explain clearly.
Find all $x$ values where $f'(x)=0$. Explain clearly.
Find all critical numbers of $f(x)$. Explain clearly.

Students 1,2 (4.1#25) $$f(x)=2x^3-3x^2-36x$$

Students 3,4 (4.1#25) $$f(x)=2x^3-3x^2-36x$$

Students 5,6 (similar to 4.1#25) $$f(x)=x^4-6x^2+5$$

Students 7,8 (4.1#29) $$f(x)=\frac{x-1}{x^2-x+1}$$

Students 9,10 (similar to 4.1#35, but easier) $$f(x)=xe^{(-3x)}$$

Students 11,12 (4.1#35) $$f(x)=x^2e^{(-3x)}$$

Students 13,14 (4.1#43) $$f(x)=x\sqrt{4-x^2}$$

Students 15,16 (4.1#47) $$f(x)=xe^{(-x^2/8)}$$

Students 17,18 (4.1#49) $$f(x)=\ln(x^2+x+1)$$

Students 19,20 (Similar to Section 4.1 Example 5 on p. 207) $$f(x)=x^{2/5}(x-7)$$

If there is time remaining: Recitation Part 2

Students do this Class Drill about Identifying Extrema

Wed Oct 25: Section 4.1: Maximum and Minimum Values ( Lecture Notes )

Fri Oct 27: Section 4.2: The Mean Value Theorem ( Lecture Notes )(Quiz Q6 )

Quiz Q6 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Two Problems, 15 points each, about Maximum and Minimum Values, based on Suggested Exercises from Section 4.1 , printed on front & back of one sheet of paper.

Mon Oct 30: Section 4.3: Derivatives and the Shapes of Graphs ( Lecture Notes )

Tue Oct 31: Recitation R10 : Sections 4.2 and 4.3

Students Solving Problems and Discussing Their Solutions

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Oct 31 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Bedell,Paris
Section 101 Student #3: Beegan,Caden
Section 101 Student #4: Brandt,Roman
Section 101 Student #5: Earl,Claire-Michael
Section 101 Student #6: Eisnaugle,Ethan
Section 101 Student #7: Jackson,Henry
Section 101 Student #8: Miller,Taylor
Section 101 Student #9: Robinson,Alana
Section 101 Student #10: Unassigned,
Section 101 Student #11: Unassigned,
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Fritz,Ronan
Section 102 Student #2: Herrmann,Mary
Section 102 Student #3: Hoffman,Sidney
Section 102 Student #4: Hubbard,Grace
Section 102 Student #5: Lavender,Kinley
Section 102 Student #6: Lindsay,Tamryn
Section 102 Student #7: Mccoy,Caleb
Section 102 Student #8: Osterlink,Bianca
Section 102 Student #9: Richardson,Ryan
Section 102 Student #10: Rickey,Jacqueline
Section 102 Student #11: Roberts,Madachi
Section 102 Student #12: Voegele,Brooklynne
Section 102 Student #13: White,Anna
Section 102 Student #14: Unassigned,
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:55pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Ngum,Venessa
Section 111 Student #10: Pickens,Charlee
Section 111 Student #11: Rasmussen,Cubbie
Section 111 Student #12: Rodean,Alex
Section 111 Student #13: Sahr,Griffin
Section 111 Student #14: Sautter,Jack
Section 111 Student #15: Wright,Beck
Section 111 Student #16: Unassigned,
Section 111 Student #17: Unassigned,
Section 111 Student #28: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Massie,Olivia
Section 112 Student #14: Miller,Austy
Section 112 Student #15: Shields,Julia
Section 112 Student #16: Smith,Kaitlyn
Section 112 Student #17: Williams,Ava
Section 112 Student #18: Unassigned,

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Slingluff,Cheyenne
Section 113 Student #16: Wenning,Luke
Section 113 Student #17: Unassigned,
Section 113 Student #18: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Dubois,Aleke
Section 114 Student #4: Elliott,Maggie
Section 114 Student #5: Hartzell,Molly
Section 114 Student #6: Kezele,Ashley
Section 114 Student #7: Lampa,Andrew
Section 114 Student #8: Mcclellan,Alex
Section 114 Student #9: Mcdermitt,Brian
Section 114 Student #10: Meyer,Morgan
Section 114 Student #11: Morris,Chase
Section 114 Student #12: Mueller,Maddy
Section 114 Student #13: Nguyen,Jim
Section 114 Student #14: Raynewater,Ty
Section 114 Student #15: Smith,Riley
Section 114 Student #16: Sobey,Lily
Section 114 Student #17: Young,Kiefer
Section 114 Student #18: Unassigned,

Rolle's Theorem: If a function $f$ satisfies the following three requirements (the hypotheses )

$f$ is continuous on the closed interval $[a,b]$.
$f$ is differentiable on the open interval $(a,b)$.
$f(a)=f(b)$.

then the following statement (the conclusion ) is true:

There is at least one number $x=c$ with $a \lt c \lt b$ such that $$f'(c)=0$$ In other words, $$\text{the slope of the tangent line at }x=c\text{ is }m=f�(c)=0$$

Remark: The theorem does not give you the value of $c$. If $c$ exists , you'll have to figure out its value.

Students 1,2: Consider the function $f(x)=x^3-3x+5$ on the interval $\left[-\sqrt{3},\sqrt{3}\right]$.

Verify that the function and the interval satisfy the three hypotheses of Rolle's Theorem. Explain clearly.
Find all numbers $c$ that satisfy the conclusion of Rolle's Theorem. Show all details clearly.
Draw a graph of $f(x)$ on the interval and draw a tangent line to illustrate your result.

Students 3,4: Consider the function $\cos{(x)}$ on the interval $[\frac{\pi}{6},\frac{13\pi}{6}]$.

Verify that the function and the interval satisfy the three hypotheses of Rolle's Theorem. Explain clearly.
Find all numbers $c$ that satisfy the conclusion of Rolle's Theorem. Show all details clearly.
Draw a graph of $f(x)$ on the interval and draw a tangent line to illustrate your result.

Students 5,6: Consider the function $f(x)=x+\frac{1}{x}$ on the interval $[\frac{1}{3},3]$.

Verify that the function and the interval satisfy the three hypotheses of Rolle's Theorem. Explain clearly.
Find all numbers $c$ that satisfy the conclusion of Rolle's Theorem. Show all details clearly.
Draw a graph of $f(x)$ on the interval and draw a tangent line to illustrate your result.

The Mean Value Theorem: If a function $f$ satisfies the following three requirements (the hypotheses )

$f$ is continuous on the closed interval $[a,b]$.
$f$ is differentiable on the open interval $(a,b)$.

then the following statement (the conclusion ) is true:

There is at least one number $x=c$ with $a \lt c \lt b$ such that $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ In other words, $$\text{slope of the tangent line at }c \ \text{ is equal to the slope of the secant line from }a\text{ to }b$$

Remark: The theorem does not give you the value of $c$. If $c$ exists , you'll have to figure out its value.

Students 7,8: Consider the function $f(x)=x^3-3x+2$ on the interval $[-2,2]$.

Verify that the function and the interval satisfy the two hypotheses of the Mean Value Theorem. Explain clearly.
Find all numbers $c$ that satisfy the conclusion of the Mean Value Theorem. Show all details clearly.
Draw a graph of $f(x)$ on the interval and draw a tangent line and a secant line to illustrate your result.

Students 9,10: Consider the function $f(x)=\ln{(x)}$ on the interval $[1,4]$.

Verify that the function and the interval satisfy the two hypotheses of the Mean Value Theorem. Explain clearly.
Find all numbers $c$ that satisfy the conclusion of the Mean Value Theorem. Show all details clearly.
Draw a graph of $f(x)$ on the interval and draw a tangent line and a secant line to illustrate your result.

Students 11,12: Consider the function $f(x)=\frac{1}{x}$ on the interval $[1,3]$.

Verify that the function and the interval satisfy the two hypotheses of the Mean Value Theorem. Explain clearly.
Find all numbers $c$ that satisfy the conclusion of the Mean Value Theorem. Show all details clearly.
Draw a graph of $f(x)$ on the interval and draw a tangent line and a secant line to illustrate your result.

Correspondence between sign behavior of $f'(x)$ on an interval $ (a,b) $ and increasing/decreasing behavior of the graph of $ f(x) $ on the interval $ (a,b) $

If $f'(x)$ is positive on an interval $ (a,b) $ then $f(x)$ is increasing on the interval $ (a,b) $.
If $f'(x)$ is negative on an interval $ (a,b) $ then $f(x)$ is decreasing on the interval $ (a,b) $.
If $f'(x)$ is zero on a whole interval $ (a,b) $ then $f(x)$ is constant on the interval $ (a,b) $.

The First Derivative Test for Local Extrema

Test 1: $f'(c)=0$ or $f'(c) DNE$. (If the number $c$ passes Test 1 , then $c$ is called a partition number for $f'(x)$.)
Test 2: $f(c)$ exists. (If the number $c$ passes both Test 1 and Test 2 , then $c$ is called a critical number for $f(x)$.)
Test 3: $f(x)$ is continuous at $c$.
Test 4: $f'(x)$ changes sign at $c$.(If the number $c$ passes Tests 1,2,3,4 , then $x=c$ is the location of a local max or local min of $f(x)$. The corresponding $y$ value, $f(c)$, is called the local max value or local max value .)

Correspondence between sign behavior of $f''(x)$ on an interval $ (a,b) $ and concavity behavior of the graph of $ f(x) $ on the interval $ (a,b) $

If $f''(x)$ is positive on an interval $ (a,b) $ then $f'(x)$ is increasing on the interval $ (a,b) $, which in turn means that $f(x)$ is concave up on the interval $(a,b)$.
If $f''(x)$ is negative on an interval $ (a,b) $ then $f'(x)$ is decreasing on the interval $ (a,b) $, which in turn means that $f(x)$ is concave cown on the interval $(a,b)$.

Related terminology: An inflection point is a point on the graph of a function where the function is continuous and the concavity changes (from up to down or from down to up).

Students 13,14: Consider the function $f(x)=\sin{(x)}-\cos{(x)}$ and the interval $[-2,2]$.

Find the intervals on which $f$ is increasing or decreasing .
Find the local maximum values and local minimum values of $f$.
Find the intervals on which $f$ is concave up or concave down .
Find the $(x,y)$ coordinates of all inflection points of $f$.

Students 15,16: Consider the function $f(x)=xe^{(-x)}$.

Find the intervals on which $f$ is increasing or decreasing .
Find the local maximum values and local minimum values of $f$.
Find the intervals on which $f$ is concave up or concave down .
Find the $(x,y)$ coordinates of all inflection points of $f$.

Students 17,18: Consider the function $f(x)=x^4-2x^2+3$.

Find the intervals on which $f$ is increasing or decreasing .
Find the local maximum values and local minimum values of $f$.
Find the intervals on which $f$ is concave up or concave down .
Find the $(x,y)$ coordinates of all inflection points of $f$.

Wed Nov 1: Section 4.4: Curve Sketching ( Handout on Graphing Strategy )( Lecture Notes )

Fri Nov 3: Section 4.5: Optimization ( Lecture Notes )(Last Day to Drop)(Quiz Q7 )

Quiz Q7 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Three Problems, 10 points each, printed on front & back of one sheet of paper.
- One Mean Value Theorem problem based on Suggested Exercises from Section 4.2 .
- One problem about Derivatives and the Shapes of Graphs, based on Suggested Exercises from Section 4.3 .
- One problem about Curve Sketching, based on Suggested Exercises from Section 4.4 .

Mon Nov 6: Section 4.6: Newton's Method ( Class Drill on Newton's Method )( Lecture Notes )

Tue Nov 7: Recitation R11 : Optimization; Newton's Method (Sections 4.5, 4.6)

Students Solving Problems and Discussing Their Solutions

Students find their Student Number in the lists below. The problems to be solved are listed farther down the page.

Student Numbers for Tue Nov 7 Recitation Meetings

Recitation Section 101 (meets Tue 8:00am – 8:55am in Morton 318 with Instructor Isaac Agyei)

Section 101 Student #1: Allen,Daylen
Section 101 Student #2: Beegan,Caden
Section 101 Student #3: Brandt,Roman
Section 101 Student #4: Earl,Claire-Michael
Section 101 Student #5: Eisnaugle,Ethan
Section 101 Student #6: Jackson,Henry
Section 101 Student #7: Miller,Taylor
Section 101 Student #8: Robinson,Alana
Section 101 Student #9: Unassigned,
Section 101 Student #10: Unassigned,
Section 101 Student #11: Unassigned,
Section 101 Student #12: Unassigned,
Section 101 Student #13: Unassigned,
Section 101 Student #14: Unassigned,
Section 101 Student #15: Unassigned,
Section 101 Student #16: Unassigned,
Section 101 Student #17: Unassigned,
Section 101 Student #18: Unassigned,

Recitation Section 102 (meets Tue 9:30am – 10:25am in Ellis 107 with Instructor Isaac Agyei)

Section 102 Student #1: Herrmann,Mary
Section 102 Student #2: Hoffman,Sidney
Section 102 Student #3: Hubbard,Grace
Section 102 Student #4: Lavender,Kinley
Section 102 Student #5: Lindsay,Tamryn
Section 102 Student #6: Mccoy,Caleb
Section 102 Student #7: Osterlink,Bianca
Section 102 Student #8: Richardson,Ryan
Section 102 Student #9: Rickey,Jacqueline
Section 102 Student #10: Roberts,Madachi
Section 102 Student #11: Voegele,Brooklynne
Section 102 Student #12: White,Anna
Section 102 Student #13: Unassigned,
Section 102 Student #14: Unassigned,
Section 102 Student #15: Unassigned,
Section 102 Student #16: Unassigned,
Section 102 Student #17: Unassigned,
Section 102 Student #18: Unassigned,

Recitation Section 103 (meets Tue 12:30pm – 1:25pm in Morton 122 with Instructor Isaac Agyei)

Section 103 Student #1: Alder,Ethan
Section 103 Student #2: Blower,Carsen
Section 103 Student #3: Hains,Amanda
Section 103 Student #4: Hawley,Frank
Section 103 Student #5: Kennedy,Quinn
Section 103 Student #6: Martis,Steve
Section 103 Student #7: Mikin,Reilly
Section 103 Student #8: Winterton,Jacob
Section 103 Student #9: Unassigned,
Section 103 Student #10: Unassigned,
Section 103 Student #11: Unassigned,
Section 103 Student #12: Unassigned,
Section 103 Student #13: Unassigned,
Section 103 Student #14: Unassigned,
Section 103 Student #15: Unassigned,
Section 103 Student #16: Unassigned,
Section 103 Student #17: Unassigned,
Section 103 Student #18: Unassigned,

Recitation Section 104 (meets Tue 2:00pm – 2:55pm in Morton 318 with Instructor Isaac Agyei)

Section 104 Student #1: Akpofure,Alexander
Section 104 Student #2: Armstrong,Graci
Section 104 Student #3: Benton,Kaleb
Section 104 Student #4: Bersagel,Via
Section 104 Student #5: Burns,J
Section 104 Student #6: Graham,Taylor
Section 104 Student #7: Griffiths,Kristen
Section 104 Student #8: Huntley,Lauren
Section 104 Student #9: King,Mason
Section 104 Student #10: Lopinsky,Iliana
Section 104 Student #11: Lucas,Madison
Section 104 Student #12: Maag,Stacie
Section 104 Student #13: Mcculloch,Thomas
Section 104 Student #14: Mcgannon,Jane
Section 104 Student #15: Neal,Daniel
Section 104 Student #16: Nestor,Nicholas
Section 104 Student #17: Vivo,Nicholas
Section 104 Student #18: Unassigned,

Recitation Section 111 (meets Tue 9:30am – 10:25am in Morton 218 with Instructor Kenny So)

Section 111 Student #1: Blankenship,Conner
Section 111 Student #2: Chaney,Alyssa
Section 111 Student #3: Christy,Carly
Section 111 Student #4: Henely,Lydia
Section 111 Student #5: Keener,Mckensie
Section 111 Student #6: Kessler,Crosley
Section 111 Student #7: Leary,Austin
Section 111 Student #8: Locke,Tyler
Section 111 Student #9: Ngum,Venessa
Section 111 Student #10: Pickens,Charlee
Section 111 Student #11: Rasmussen,Cubbie
Section 111 Student #12: Rodean,Alex
Section 111 Student #13: Sahr,Griffin
Section 111 Student #14: Sautter,Jack
Section 111 Student #15: Wright,Beck
Section 111 Student #16: Unassigned,
Section 111 Student #17: Unassigned,
Section 111 Student #18: Unassigned,

Recitation Section 112 (meets Tue 11:00am – 11:55am in Ellis 107 with Instructor Kenny So)

Section 112 Student #1: Alsko,Adam
Section 112 Student #2: Altiere,David
Section 112 Student #3: Beya,Mimi
Section 112 Student #4: Byrd,Iana
Section 112 Student #5: Collins,Kian
Section 112 Student #6: Gonzales,Solana
Section 112 Student #7: Hellmich,Adam
Section 112 Student #8: Horgan,Ruby
Section 112 Student #9: Ijoma,Lillian
Section 112 Student #10: Jones,Cate
Section 112 Student #11: Jotia,Zinzi
Section 112 Student #12: Lenz,Wyatt
Section 112 Student #13: Massie,Olivia
Section 112 Student #14: Miller,Austy
Section 112 Student #15: Shields,Julia
Section 112 Student #16: Smith,Kaitlyn
Section 112 Student #17: Williams,Ava
Section 112 Student #18: Unassigned,

Recitation Section 113 (meets Tue 2:00pm – 2:55pm in Morton 126 with Instructor Kenny So)

Section 113 Student #1: Berry,Jaden
Section 113 Student #2: Brand,Kylee
Section 113 Student #3: Cattani,Ella
Section 113 Student #4: Davis,Ethan
Section 113 Student #5: Duncan,Ellora
Section 113 Student #6: Espinueva,Shirleen
Section 113 Student #7: Fisher,Hunter
Section 113 Student #8: Frizzell,Leah
Section 113 Student #9: Hagstrom,Steven
Section 113 Student #10: Ingraham,Emma
Section 113 Student #11: Johnson,Josh
Section 113 Student #12: Mccall,Lauren
Section 113 Student #13: Miles,Abby
Section 113 Student #14: Mullins,Kaitlyn
Section 113 Student #15: Slingluff,Cheyenne
Section 113 Student #16: Wenning,Luke
Section 113 Student #17: Unassigned,
Section 113 Student #18: Unassigned,

Recitation Section 114 (meets Tue 3:30pm – 4:25pm in Morton 122 with Instructor Kenny So)

Section 114 Student #1: Angerstien,Blake
Section 114 Student #2: Blair,Natalie
Section 114 Student #3: Dubois,Aleke
Section 114 Student #4: Elliott,Maggie
Section 114 Student #5: Hartzell,Molly
Section 114 Student #6: Kezele,Ashley
Section 114 Student #7: Lampa,Andrew
Section 114 Student #8: Mcclellan,Alex
Section 114 Student #9: Mcdermitt,Brian
Section 114 Student #10: Meyer,Morgan
Section 114 Student #11: Morris,Chase
Section 114 Student #12: Mueller,Maddy
Section 114 Student #13: Nguyen,Jim
Section 114 Student #14: Raynewater,Ty
Section 114 Student #15: Smith,Riley
Section 114 Student #16: Sobey,Lily
Section 114 Student #17: Young,Kiefer
Section 114 Student #18: Unassigned,

Meeting Part 1: Optimization Problems (Section 4.5)

Students 1,2: (Suggested Exercise 4.5#2) Find two numbers whose difference is 100 and whose product is a minimum. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 3,4: (Suggested Exercise 4.5#7) Find the dimensions of a rectangle with perimeter 100m whose area is as large as possible. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 5,6: (Suggested Exercise 4.5#11) If 1200 cm ² of material is available to make a box with a square base and an open top, find the largest possible volume of the box. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 7,8: (Suggested Exercise 4.5#15) Find the point on the line $y=2x+3$ that is closest to the origin. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 9,10: (Suggested Exercise 4.5#17) Find the points on the ellipse $4x^2+y^2=4$ that are farthest away from the point $(1,0)$ (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 11,12: (Suggested Exercise 4.5#22)Find the area of the largest rectange that can be inscribed in a right triangle with legs of lengths 3cm and 2cm if two sides of the rectangle lie along the legs. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 13,14: (Suggested Exercise 4.5#25) A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window that has the greatest area. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 15,16: (Suggested Exercise 4.5#30) A cone-shaped paper drinking cup is to be made to hold 27 cm ³ of water. Find the height and radius of the cup that will use the smallest amount of paper. (You must use calculus and show all details clearly. No credit for just guessing values.)

Students 17,18: (Suggested Exercise 4.5#39) Find an equation of the line through the point $(3,5)$ that cuts off the least area from the first quadrant. (You must use calculus and show all details clearly. No credit for just guessing values.)

Meeting Part 2: Newton's Method (Section 4.6)

Students work in pairs on this ( Class Drill on Using Newton's Method )

Wed Nov 8: Section 4.7: Antiderivatives ( Lecture Notes )

Fri Nov 10: Holiday

Mon Nov 13: Exam X3 Covering Section Chapter 4

Exam X3 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
The Exam will last the full duration of the class period.
No books, notes, calculators, or phones
Five problems, printed on front & back of three sheets of paper. All problems are based on suggested exercises.
1. A problem about Maximum and Minimum Values (Section 4.1)
2. A problem about Derivatives and the Shapes of Graphs and/or Curve Sketching (Sections 4.3 and 4.4)
3. A problem about Optimization (Section 4.5)
4. A problem about Newton's Method (Section 4.6)
  - Note: I will not give you the formula to use for Newton's Method. The formula is presented in the Book, and it was presented in Lecture and in Recitation. You should learn the formula by doing exercises that require you to use the formula. There are exercises of this type in the Homework List , and you did Class Drills in Class on Mon Nov 6 and in Recitation on Tue Nov 7. You can see those Class Drills in the calendar entries for those days.
5. A problem about Antiderivatives (Section 4.7)
  - Note: I will not give you the give you the Basic Antidifferentiation Formulas . The formulas are presented in the Book, and they were presented in Lecture. You should learn those formulas by doing exercises that require you to use those formulas. There are exercises of this type in the Homework List .

Reminders about Studying

The most important issue is, Can you successfully write down the solution to a problem? Therefore, the centerpiece of your studying should be, Practicing writing down the solutions to problems.
Mathematical concepts get presented to you in the Book and in Lecture . Examples are also presented in both places. I generally try to not present a particular type of example in class if a similar example is already presented well in the book. Rather, I try to present examples in class that are different from the examples that are presented in the book. Therefore, for your studying, you should be sure to study not just the examples that I do in class, but also the examples that are presented in the book!
The book and my lectures are not supposed to present examples similar to all of the kinds of problems that you need to know how to solve. The idea is that the book and my lectures teach you the concepts and show you some examples, and from there, you need to be able to generalize and solve different problems.
In writing my Quizzes and Exams , I aim to include a mixture of
- Problems that are based on problems from the Homework List and that are similar to a class example .
- Problems that are based on problems from the Homework List and that are not similar to a class example , but that are similar to a book example .
- Problems that are based on problems from the Homework List but that are not similar to any class or book example .
Therefore, your studying and practice problems should include studying and practicing of all types of problems.

Tue Nov 14: Recitation R12 : Antiderivatives, Position, Velocity, Acceleration (Section 4.7 Leftovers)

Students work in pairs on common problems.

All students in the room work on problem [1] for about 5 minutes, then the Instructor discusses that problem. Then all students work on problem [2] for 5 minutes, and the Instructor discusses that problem, and so on. Some problems will need more time.

Meeting Part 1: Antiderivatives Satisfying an Extra Condition (Section 4.7)

[1] (Suggested Exercise 4.7 #15) Let $$f(x)=7x-3x^5$$

Find the General Antiderivative , $F(x)$.
Find the Particular Antiderivative that satisfies $F(1)=5$.

[2] (not like a book exercise) Let $$f(t)=3e^t-4$$

Find the General Antiderivative , $F(t)$.
Find the Particular Antiderivative that satisfies $F(0)=8$.

[3] (review of prerequisites) Draw the first quadrant of the unit circle , with important famous angles $\theta=0,\pi/6,\pi/4,\pi/3,\pi/2 $ shown, along with the $(x,y)$ coordinates of the points where the rays of those angles intersect the circle.

[4] (4.7#27) Find $f(t)$ such that $$f'(t)=10\cos t - \sec^2 t \ \text{ for } \ -\pi/2 \lt t \lt \pi/2 \ \text{ and that } \ f(\pi/3)=13$$

[5] (4.7#20) Suppose that $$f''(x)=30x-\sin x$$ Find $f(x)$.

Problems about Position , Velocity , and Acceleration

Remember that for an object moving in one dimension, the velocity , $v(t)$, is the derivative of the position , $s(t)$. That is, $$s'(t) = v(t)$$

Therefore, position , $s(t)$, is an antiderivative of the velocity , $v(t)$.

Also remember that the acceleration , $a(t)$, is the derivative of the velocity , $v(t)$.

Therefore, velocity , $v(t)$, is an antiderivative of the acceleration , $a(t)$.

Furthermore, recall that when an object falls freely under the influence of gravity , it is known that the object will have constant acceleration with a value $$a=-32 \ \text{ft/s}^2$$ The negative sign may be confusing. The reason for the negative sign is that the positive position direction is up . Since gravity makes objects fall down , it is acclerating them in the negative position direction. Hence, the acceleration gets a negative sign.

[6] (based on 4.7#40, similar to 4.7#47) Suppose that an object is moving in one dimension with velocity $$v(t)=9\sqrt{t} \ \text{ ft/s}$$

Find the general form of the position function , $s(t)$. That is, find the General Antiderivative of $v(t)$, but instead of calling it $V(t)$, call it $s(t)$.
Suppose that it is also known that the initial position is $s(0)=13 \ \text{ft}$. Find the position function . That is, find the Particular Antiderivative that satisfies $s(0)=13$.

[7] (based on 4.7#43) Suppose that an stone is dropped off a tower that is 400 feet tall and falls freely. Let position be defined to be zero at ground level , and remember that the positive position direction is up .

What is the value of the initial position of the stone, $s(0)$?
What is the value of the initial velocity of the stone, $v(0)$?
The acceleration of the stone is constant. What is the value of the the acceleration , $a$?
Given that the velocity , $v(t)$, is an antiderivative of the acceleration , find the general form of the velocity function , $v(t)$. That is, find the General Antiderivative of $a(t)$, but instead of calling it $A(t)$, call it $v(t)$.
Knowing what you know about the initial velocity , $v(0)$, find the particular form of the velocity function , $v(t)$. That is, find the Particular Antiderivative of $a(t)$ that satisfies $$v(0) = \text{ initial velocity that you identified earlier}$$
Given that the position , $s(t)$, is an antiderivative of the velocity , find the general form of the position function , $s(t)$. That is, find the General Antiderivative of $v(t)$, but instead of calling it $V(t)$, call it $s(t)$.
Knowing what you know about the initial position , $s(0)$, find the particular form of the position function , $s(t)$. That is, find the Particular Antiderivative of $v(t)$ that satisfies $$s(0) = \text{ initial position that you identified earlier}$$ The formula that you have found for the position function , $s(t)$ gives the position of the stone above ground level at time $t$.
What is the time when the stone reaches ground level?
What is the speed of the stone when it strike the ground?

Wed Nov 15: Section 5.1: Areas and Distances ( Lecture Notes )( Class Drill on Riemann Sums )

Fri Nov 17: Section 5.2: The Definite Integral ( Lecture Notes )

Mon Nov 20: Section 5.3: Evaluating Definite Integrals ( Lecture Notes )(Quiz Q8 )

Quiz Q8 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Two Problems, 15 points each, printed on front & back of one sheet of paper.
1. A Problem about Areas and Distances, based on Suggested Exercises from Section 5.1 .
2. A problem about Definite Integrals, based on Suggested Exercises from Section 5.2 .

Tue Nov 21: Recitation R13 : The Definite Integral (Section 5.2) and Evaluating Definite Integrals (Section 5.3)

Students work in pairs on common problems.

All students in the room work on problem [1] for about 10 minutes, then the Instructor discusses that problem. Then all students work on problem [2] for 10 minutes, and the Instructor discusses that problem, and so on. Some problems will need more time.

[1]: Students work in pairs on this Class Drill : Definite Integrals for a Graph Made Up of Geometric Shapes

[2]: Students work in pairs on this Class Drill : Computing Definite Integrals Using Geometry

Recall The Evaluation Theorem (ET)

(the relationship between definite integrals and antiderivatives )

If $f(x)$ is continuous on the interval $[a,b]$, then $$\int_a^bf(x)dx\underset{\text{ET}}{=}F(b)-F(a)$$ where $F(x)$ is any antiderivative of $f(x)$.

Use the Evaluation Theorem to evaluate the integrals. Show all details clearly and use correct notation.

Basic Problems

[3]: (5.3#3)$$\int_{-2}^{0}\left(\frac{1}{2}t^4+\frac{1}{4}t^3-t\right)dt$$

[4]: (5.3#13)$$\int_{1}^{2}\left(\frac{x}{2}-\frac{2}{x}\right)dx$$

[5]: (5.3#7)$$\int_{0}^{\pi}\left(5e^x+3\sin x\right)dx$$

Harder Problems that Involve Rewriting the Integrand Before Integrating

[6]: (5.3#18)(A lot of rewriting on this one, but it results in a very simple integral!) $$\int_{0}^{\pi/3}\left(\frac{\sin \theta +\sin \theta \tan^2 \theta}{\sec^2 \theta}\right)d\theta$$

[7]: (5.3#9) $$\int_{1}^{4}\left(\frac{4+6u}{\sqrt{u}}\right)du$$

[8]: (5.3#23)$$\int_{1}^{e}\left(\frac{x^2+x+1}{x}\right)dx$$

Wed Nov 22: Holiday

Fri Nov 24: Holiday

Mon Nov 27: Section 5.3: Evaluating Definite Integrals ( Lecture Notes )

Tue Nov 28: Recitation R14 : Evaluating Definite Integrals (Section 5.3)

Students work in pairs on common problems.

Recitation Part 1: Using the Evaluation Theorem

Recall The Evaluation Theorem (ET) as presented in the book and in lecture on Mon Nov 20, using the terminology of antiderivatives :

(the relationship between definite integrals and antiderivatives )

If $f(x)$ is continuous on the interval $[a,b]$, then $$\int_a^bf(x)dx\underset{\text{ET}}{=}F(b)-F(a)$$ where $F(x)$ is any antiderivative of $f(x)$.

And recall The Evaluation Theorem (ET) re-cast using the notation of indefinite integrals , as presented in the book and in lecture on Mon Nov 27:

(the relationship between definite integrals and indefinite integrals )

If $f(x)$ is continuous on the interval $[a,b]$, then

$$\int_a^bf(x)dx\underset{\text{ET}}{=}\left. \left(\int f(x)dx\right)\right\vert_a^b$$

Use the Evaluation Theorem to evaluate these three basic definite integrals. Show all details clearly and use correct notation.

[1]: (5.3#11) $$\int_{0}^{1}x\left(\sqrt[3]{x}+\sqrt[4]{x}\right)dx$$ Give an exact answer and a decimal approximation , rounded to 3 decimal places.
Hint: You�ll have to rewrite the integrand as a sum of power functions before integrating.

[2]: (5.3#15) $$\int_{0}^{1}\left(x^{10}+10^x\right)dx$$ Give an exact answer and a decimal approximation , rounded to 3 decimal places.
Hint: You�ll have to do some sleuth work to figure out one of the antiderivatives. Try checking your book in Section 5.3.

[3]: (5.3#29) $$\int_{-1}^{2}\left(x-2|x|\right)dx$$ Give an exact answer .
Hint: Remember that the function $|x|$ is a piecewise-defined function. That is, the formula for $|x|$ depends on which piece of the domain that you are in. That will mean that you will need to break up this definite integral on the interval $[-1,2]$ into two definite integrals, each on a smaller interval.

Recitation Part 2: Using the Net Change Theorem

Recall The Net Change Theorem (NCT) as presented in the book and in lecture on Mon Nov 27, using the terminology of antiderivatives :

(the integral of a rate of change of a quantity is the net change of that quantity )

If $F(x)$ is differentiable on the interval $[a,b]$, then $$\int_a^bF'(x)dx\underset{\text{NCT}}{=}F(b)-F(a)$$

[4]: (5.3#51) If $w'(t)$ is the rate of growth of a child in pounds per year, what does the integral below represent? $$\int_{5}^{10}w'(t)dt$$

[5]: (5.3#52) If oil leaks from a tank at a rate of $r(t)$ gallons per minute at time $t$, what does the integral below represent? $$\int_{0}^{120}r(t)dt$$

[6]: (5.3#59) An object moves along a line with velocity $$v(t)=3t-5 \ \text{ for } \ 0\leq t \leq 3$$

Find the displacement of the object during the time interval. Give an exact answer .
Illustrate your result for (a) using a graph of the velocity $v(t)$.
Find the distance traveled by the object during the time interval. Give an exact answer and a decimal approximation , rounded to 3 decimal places.

[7]: (5.3#60) An object moves along a line with velocity $$v(t)=t^2-2t-3\ \text{ for } \ 0\leq t \leq 6$$

Find the displacement of the object during the time interval $[2,5]$. Give an exact answer .
Illustrate your result for (a) using a graph of the velocity $v(t)$.
Find the distance traveled by the object during the time interval $[2,5]$. Give an exact answer and a decimal approximation , rounded to 3 decimal places.

Wed Nov 29: Section 5.4: The Fundamental Theorem of Calculus ( Lecture Notes )( Class Drill: Area Function )

Fri Dec 1: Section 5.4: The Fundamental Theorem of Calculus ( Lecture Notes )(Quiz Q9 )

Quiz Q9 Information

Section 100: Sit in Alternate Seats and rows in Morton 235
Section 110: Sit in Alternate Seats and rows in Morton 237
20 Minutes at the end of class
No books, notes, calculators, or phones
Three Problems, 10 points each, printed on front & back of one sheet of paper.
1. A Problem about Evaluating Definite Integrals, based on Suggested Exercises from Section 5.3 .
2. A Problem about Evaluating Definite Integrals, based on Suggested Exercises from Section 5.3 .
3. A problem about the Fundamental Theorem of Calculus, based on Suggested Exercises from Section 5.4 .

Mon Dec 4 Section 5.5: The Substitution Rule ( Lecture Notes )( Handout on Substitution Method )

Tue Dec 5: Recitation R15 : The Fundamental Theorem of Calculus and the Substitution Rule (Sections 5.4 and 5.5)

Recitation Part 1: Using the Fundamental Theorem of Calculus, Part 1

Recall the Fundamental Theorem of Calculus, Part 1

If $f$ is continuous on the interval $[a,b]$, then $$\frac{d}{dx}\left(\int_a^xf(t)dt\right)\underset{\text{FTC1}}{=}f(x) \text{ for } \ a \lt x \lt b$$

[1]: (5.4#6) The function $g(x)$ is defined by the integral: $$g(x)=\int_{3}^{x}e^{t^2-t} \ dt$$ Find $g'(x)$.

[2]: (5.4#10) The function $g(x)$ is defined by the integral: $$g(x)=\int_{0}^{x}\sqrt{1+\sqrt{t}} \ dt$$ Find $g'(x)$.

[3]: (5.4#10) The function $h(x)$ is defined by the integral: $$h(x)=\int_{0}^{\tan x}\sqrt{1+\sqrt{t}} \ dt$$ (Hint: You will need the Chain Rule .)

Recitation Part 2: Computing the Average Value of a Function on an Interval

Recall the Definition of the Average Value of a Function on an Interval

If $f(x)$ is continuous on the interval $[a,b]$, then the Average Value of $f(x)$ on the interval $[a,b]$ is defined to be the number

$$h=\frac{1}{b-a}\int_a^bf(x)dx$$

[4]: Find the average value of the function $f(x)= \frac{1}{x}$ on the interval $[1,4]$. Simplify your answer.

[5]: Find the average value of the function $f(x)= \sin (x) $ on the interval $[0,\pi]$. Simplify your answer.

[6]: Find the average value of the function $f(x)= \sec^2(\theta)$ on the interval $[0,\pi/4]$. Simplify your answer.

Recitation Part 3: The Substitution Method

Recall The Substitution Method as Introduced in Monday�s Lecture

Handout on Substitution Method

[7]: (5.5#3) Find the Indefinite Integral by using the Substitution Method . $$\int x^4 \sqrt{1+x^5} \ dx$$

[8]: (5.5#13) Find the Indefinite Integral by using the Substitution Method . $$\int \frac{1}{7-5x} \ dx$$

[9]: (5.5#19) Find the Indefinite Integral by using the Substitution Method . $$\int e^x \sqrt{1+e^x} \ dx$$

[10]: (5.5#20) Find the Indefinite Integral by using the Substitution Method . $$\int \cos^4 \theta \sin \theta \ d\theta$$

[11]: (5.5#27)

( Review ) Use the Chain Rule or the Quotient Rule to find the derivative of $\sec x$. (Either rule can be used. One is simpler.)
Find the Indefinite Integral by using the Substitution Method . $$\int \sec^3 x \tan x \ dx$$ ( Hint: Rewrite the integrand as $\sec^2 x \sec x \tan x $.)

Wed Dec 6: Section 5.5: The Substitution Rule ( Lecture Notes )

Fri Dec 8: Review ( Lecture Notes )

Thu Dec 14: Combined Final Exam FX from 2:30pm – 4:30pm

Section 100 (Mon, Wed, Fri 8:35am) will have its final in its usual room, Morton 235. Seating will be in Alternate Seats and Alternate Rows.
Section 110 (Mon, Wed, Fri 10:45am) will have its final in its usual room, Morton 237. Seating will be in Alternate Seats and Alternate Rows.

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2023 – 2024 Fall Semester MATH 2301 Calculus I Sections 100 and 110

Section 100 is a Lecture Section, taught by Mark Barsamian.

Associated to Lecture Section 100 are four Recitation Sections, led by Isaac Agyei

Section 110 is a Lecture Section, taught by Mark Barsamian.

Associated to Lecture Section 110 are four Recitation Sections, led by Kenny So

Link to download a PowerPoint presentation with Instructions for Setting Up WebAssign: Link

Exercises for Fall 2023 MATH 2301 Sections 100 and 110 (Barsamian) (from Stewart Essential Calculus Early Transcendentals 2nd Edition)Your goal should be to write solutions to all 333 exercises in this list.

Grading System for MATH 2301 Sections 100 and 110 (Barsamian) 2023 – 2024 Fall Semester

There is no grade curving in this course.

Two things that are not part of your Course Grade

Grade Calculation Worksheet

Attendance Policy: Show/Hide Attendance Policy

Electronic Communication Policy (For both Students and Instructors): Show/Hide Communication Policy

Policy on Cheating: Show/Hide Policy

Calendar for MATH 2301 Sections 100 and 110 (Barsamian) 2023 – 2024 Fall Semester

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Sep 5 Recitation Meetings

The Problems to Be Done in Tue Sep 5 Recitation Meetings

Limits that are Indeterminate Forms and that require no trick, just messy work

Limits that Involve Rationalizing

Limits that Involve Absolute Value

Limits that Involve the Squeeze Theorem

Limits that Use Famous Fact that $$\lim_{x\rightarrow 0}\frac{\sin{(x)}}{x}=1$$

Quiz Q1 Information

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Sep 5 Recitation Meetings

The Problems to Be Done in Tue Sep 12 Recitation Meetings

Students #1, 2:

Students #3,4:

Students #5,6:

Students #7,8

Students #9,10

Students: #11,12:

Students: #13,14

Students: #15,16

Students: #17,18

Students: #19,20

Quiz Q2 Information

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Sep 19 Recitation Meetings

The Problems to Be Done in Tue Sep 19 Recitation Meetings

Exam X1 Information

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Sep 26 Recitation Meetings

Basic Derivative Formulas

First Problems to Be Done in Tue Sep 26 Recitation Meetings: Derivatives

Second Problems to Be Done in Tue Sep 26 Recitation Meetings: Tangent Lines and Normal Lines

Quiz Q3 Information

Student Numbers for Tue Oct 3 Recitation Meetings

Basic Derivative Formulas Show/Hide Formulas

Part 1: Students Solving Problems and Discussing Their Solutions Show/Hide Part 1

Part 2: Conceptual Questions about Tangent Lines Show/Hide Part 2

Quiz Q4 Information

Student Numbers for Tue Oct 10 Recitation Meetings

Basic Derivative Formulas Show/Hide Formulas

Students Solving Problems and Discussing Their Solutions

Each student will solve two problems: One problem in Round 1 , and another problem in Round 2 .

Problems for Oct 10 Round 1 Show/Hide Round 1

Problems for Oct 10 Round 2 Show/Hide Round 2

Quiz Q5 Information

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Oct 17 Recitation Meetings Show/Hide Student Numbers

Derivative Formulas That We Know So Far Show/Hide Formulas

Each student will solve two problems.

Round 1 Show/Hide Round 1

Round 2 Show/Hide Round 2

Exam X2 Information

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Oct 24 Recitation Meetings Show/Hide Student Numbers

Recitation Part 1: Finding Critical Numbers of Functions Show/Hide Part 1

Each student will answer questions related to finding the critical numbers of a function.

If there is time remaining: Recitation Part 2 Show/Hide Part 2

Quiz Q6 Information

Students Solving Problems and Discussing Their Solutions

Student Numbers for Tue Oct 31 Recitation Meetings Show/Hide Student Numbers

Correspondence between sign behavior of \(f'(x)\) on an interval \( (a,b) \) and increasing/decreasing behavior of the graph of \( f(x) \) on the interval \( (a,b) \)

The First Derivative Test for Local Extrema

Correspondence between sign behavior of \(f''(x)\) on an interval \( (a,b) \) and concavity behavior of the graph of \( f(x) \) on the interval \( (a,b) \)

Quiz Q7 Information

Students Solving Problems and Discussing Their Solutions

Exercises for Fall 2023 MATH 2301 Sections 100 and 110 (Barsamian)
(from Stewart Essential Calculus Early Transcendentals 2nd Edition)
Your goal should be to write solutions to all 333 exercises in this list.

Attendance Policy:

Electronic Communication Policy (For both Students and Instructors):

Policy on Cheating:

Basic Derivative Formulas

Part 1: Students Solving Problems and Discussing Their Solutions

Part 2: Conceptual Questions about Tangent Lines

Basic Derivative Formulas

Problems for Oct 10 Round 1

Problems for Oct 10 Round 2

Student Numbers for Tue Oct 17 Recitation Meetings

Derivative Formulas That We Know So Far

Round 1

Round 2

Student Numbers for Tue Oct 24 Recitation Meetings

Recitation Part 1: Finding Critical Numbers of Functions

If there is time remaining: Recitation Part 2

Student Numbers for Tue Oct 31 Recitation Meetings

Student Numbers for Tue Nov 7 Recitation Meetings