\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Suppose
$f_n(x)=x^n 2^{-x}$. Graph $f_n(x)$ for $0 \leq x\leq 10$ and
$n=1,2,3$. You may need to adjust the viewing window to see the
graph. Describe how the graphs change as $n$ increases. What features
stay the same?  Find the $x$ coordinate $x_{\rm max}$ of the highest
point of the graph for $n = 1,2,3$.  Plot $x_{\rm max}$ as a function
of $n$. Guess what the graph of $f_{5}(x)$ looks like, and what the
$x$ coordinate of the highest point is. Then test your guess by
actually generating the graph.

\medskip

\noindent b) Suppose $g_n(x)=x2^{-nx}$. Graph $g_n(x)$ for $0 \leq
x\leq 10$ and $n=1,2,3$. You may need to adjust the viewing window to
see the graph. Describe how the graphs change as $n$ increases. What
features stay the same?  Find the $x$ coordinate $x_{\rm max}$ of the
highest point of the graph for $n = 1,2,3$.  Plot $x_{\rm max}$ as a
function of $n$. Guess what the graph of $g_{5}(x)$ looks like, and
what the $x$ coordinate of the highest point is. Then test your guess
by actually generating the graph.











\vfil\eject\end