\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose that $f(x)=e^{-Ax}$, where
$A$ is a positive real number.

\medskip

\noindent a) Show that the integral $\int_1^2 f(x) \, dx\to 0$ as
$A\to\infty$. (You may wish to draw a picture, but other verification
is also necessary.)

\medskip

\noindent b) Show that the integral $\int_1^2 x f(x) \, dx\to 0$ as
$A\to\infty$. (You may wish to draw a picture, but other verification
is also necessary.)

\medskip

\noindent c) Show that the integral $\int_1^2 {1 \over {1+5 x^{48}}}
f(x) \, dx\to 0$ as $A\to\infty$. (You may wish to draw a picture, but
other verification is also necessary.) 

\smallskip

\noindent {\bf Note} It isn't always necessary or even possible to
compute every integral exactly. But this integral can be {\it
estimated}\/ to get enough information.

\vfil\eject\end