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\title{Engineering and Science Mathematics 1A}
\author{Review for Midterm I}
\date{Exam date: October 5, 2010}
\maketitle

\begin{enumerate}
\item Limits, one-sided limits.  Typical questions include p.\ 97 no.\
30, 35, or the computation of the limit
\[
  \lim_{x\to\infty} e^{-x} \, \ln x \,.
\]
Be familiar with the ``squeeze law'' and its application.

\item Continuity: When is a function continuous, can a discontinuous
function be extended to be continuous?  Can you show that
differentiability implies continuity?  

Practice question: How can you define $f(0)$ of the function
\[
  f(x) = x^2 \, \sin \frac1x
\]
so that $f$ is a continuous function?  Is the resulting function
differentiable at $x=0$?  If so, what is its derivative?  Is the
derivative continuous?

\item Derivative: Definition, compute the derivative in simple cases
as the limit of a difference quotient; differentiation rules;
derivatives of trigonometric functions, log, exp.

\item Applied minimax problems (lots of practice examples on pages 158
and 159 on the Homework 4 handout).

\item Curve sketching:  Finding critical points; when does a critical
point correspond to a minimum, when to a maximum?  Concavity, Points
of inflection.  See Homework 4 problems.


\end{enumerate}

Exam rules:
\begin{itemize}
\item No notes and calculators.
\item Paper will be supplied.
\item Respect the Code of Academic Integrity.  It will be enforced.
\end{itemize}
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