\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Consider the function $f(x)= e^x
\sin Nx$ \underbar{on the interval} $[0,1]$ where $N$ is a positive
integer.

\medskip

\noindent a) With a sketch or otherwise, describe the graph of this
function when $N=5$, $N=10$, and $N=100$.

\medskip

\noindent b) Compute $\int_0^1 f(x)\, dx$. Evaluate this integral when
$N=5$, $N=10$, and $N=100$.

\medskip

\noindent c) What happens to the graph and to the value of the
integral as $N\to\infty$? Does the graph confirm the limiting behavior
of the integral's value?

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