%Limits
%If you modify this file, please indicate here and in the footnote.
%Math263A
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\begin{document}
\begin{center}
{\Large
Limits\footnote{Copyright \copyright 2002 Larry Snyder and Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
\end{center}
\begin{enumerate}
\item Try the following commands (at the prompt and
press \fbox{Enter}):
\begin{enumerate}
\item \verb&x = sym('x')&
\item \verb&f = x^2&
\item \verb&limit(f, 2) &
\item \verb&limit(f, inf)&
\item \verb&limit(1/x, inf)&
\item \verb&limit(log(abs(x)), 0)&
\item \verb&limit(1/x, 0)&
\item Explain what happened in each example, that is,
why did it give the answer it did.
\end{enumerate}
\vspace{.2cm}
\item Use \textsc{MatLab} to find the limits of the following functions
at the given points:
\begin{enumerate}
\item $\sqrt{x}$ at x = 0
\qquad (Type as: \verb$ limit(sqrt(x), 0)$)
\item $\sqrt{x^2 - .00001}$ at x = 0
\qquad (Type as: \verb$ limit(sqrt(x^2 - .00001), 0)$)
\item $\sqrt{x}$ at x = -1
\qquad (Type as: \verb$ limit(sqrt(x) , -1)$)
\item $\sin x$ at x = inf
\qquad (Type as: \verb$ limit(sin(x), inf)$)
\item $\sin(1/x)$ at x = 0
\qquad (Type as: \verb$ limit(sin(1/x), 0)$)
\item Explain what happened in each example.
\end{enumerate}
\vspace{.2cm}
\item Prepare a brief (\verb$< $1 page) written report answering all
the questions. Use complete sentences and standard mathematical notation.
Do {\bf not} get a printout.
\end{enumerate}
\vfill
\noindent
\textsf{The user encounters usual limits, limits at infinity
and infinite limits, complex limits and oscillatory functions.
}
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