\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Use your calculator to try to figure out what might be
the value of 
$$
\lim_{x\to 0}{ {(\cot\, x)(1 - \cos\,2x)}\over{x}}
$$
by tracing the graph of ${(\cot\,x)(1 - \cos\,2x)}\over x$ for $x$ near
$0$. Show the graph. Then find the exact value of the limit by using a
computation based on trig formulas and the fact that $\lim\limits_{\theta \to
0} {{\sin\,\theta}\over{\theta}} = 1$.









\vfil\eject\end