\def\wsn{6}
\input worksheet.tex

\item{1.}  Compute the following limits algebraically:
$$
\pt a \lim_{x\to2}{|x-2|\over x^2-2x}\hskip1in
\pt b \lim_{x\to-1^+}{|x+1|\over x^3+1}\hskip1in
\pt c \lim_{x\to2}{(x-2)^2\over|x-2|}
$$
{\it Note: These are all previous exam problems!}

\bigskip
\hbox{\vbox{\hsize=3.7in
\itemitem{2.\hskip12pt a)}  In the unit circle to the right, find the
area of triangle $OBC$, the area of triangle $ODA$, and the area of
the sector of the circle $OBA$ all as functions of $\theta$.

\bigskip
\itemitem{b)}  Use the Squeeze Theorem to find $\displaystyle
\lim_{\theta\to0}{\sin\theta\over\theta}{\atop.}$
\vskip.4in}\hskip.4in
\epsfxsize=1.6in\epsfbox{/home/oehrtman/m210/sincircle.eps}}


\bigskip
\item{3.}  Use your result from Problem 3 to compute
$\displaystyle\lim_{\theta\to0}{1-\cos\theta\over\theta}$
algebraically. 

\item{} Hint: multiply by a clever form of one.

\bigskip\bigskip\bigskip
\itemitem{4.\hskip12pt a)}  Find the slope of the secant line
intersecting the graph of $f(x)=\sin x$ at $x$ and $x+h$.

\medskip
\itemitem{b)}  Simplify your expression using the identity 
$$
\sin(A+B)=\sin A\cos B+\sin B\cos A.
$$ 

\itemitem{c)}  Compute the limit of these slopes as $h\to0$.

\bigskip\bigskip\bigskip
\item{5.}  Let $\displaystyle f(x)=\cases{1&$x\geq2$;\cr\cr x&$x<2$.\cr}$

\medskip
\itemitem{a)}  Find a formula giving the slope of the secant line
intersecting $f(x)$ when $x=2$ and $x=2+h$.

\smallskip
\itemitem{} Note: You will have different answers for $h<0$ and
$h>0$.  Why?

\medskip
\itemitem{b)}  Find the limit of these slopes as $h\to0^-$ and $h\to0^+$.


\bigskip\bigskip\bigskip
\item{6.}  A cake has dimensions $15''\times15''\times3''$.  It is
frosted on the sides and top.  How can it be divided into $5$ pieces
so that each piece has the same amount of cake and the same amount of
frosting?  What if the dimensions are changed?  What about $6$ pieces?
$7$ pieces?  $n$ pieces?




\bye