\def\wsn{5}
\input worksheet.tex

\item{1.}  Use algebraic techniques to compute the following limits.
Show all your steps! 
$$
\eqalign{
\pt a &\lim_{x\to1}{x^3-5x^2+8x-4\over x^3-x^2-4x+4}\cr\cr
\pt c &\lim_{x\to3^-}{|x-3|\over9-x^2}\cr}\hskip1in
\eqalign{
\pt b &\lim_{x\to2}\left({1\over x-2}-{4\over x^2-4}\right)\cr\cr
\pt d &\lim_{x\to-1}{x^4+x\over x^2+x}\cr}
$$
{\it Note: These have all appeared on Dr. Davis's previous exams.}

\bigskip
\item{2.}  {\bf The Squeeze Theorem: } Suppose $u(x)$ and $v(x)$ are
functions which are defined for $c{\pi\over2}$.\cr} 
$$
Graph $f_t$ for every value of $t$ for which $f_t$ is continuous.


\bigskip
\item{7.}  {\bf More limits!} Compute
$$
\pt a \lim_{x\to1}{1-{1\over x}\over1-{1\over\sqrt x}}\hskip.5in
\pt b \lim_{x\to1}\left({1\over x}-1\right)\left({x\over x-1}\right)\hskip.5in
\pt c \lim_{x\to2}{\sqrt{x+2}-2\over x-2}
$$


\bye