\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Suppose $A$ is a positive real
number and $m_A$ is the average value of $\left(
\sin(Ax)\vphantom{)^3}\right)^3$ on the interval $[0,2]$. Compute
$m_A$.

\medskip

\noindent {\bf Note} The answer will have several terms and will {\it
not}\/ be simple.

\medskip

\noindent b) What is $\lim\limits_{A\to \infty}m_A$?

\medskip

\noindent {\bf Note} This answer {\it should}\/ be simple. Explain
briefly why it is correct. You may refer to graphs of functions if
that is helpful.

\vfil\eject\end