\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Suppose $f(x)=3^x$. Plot $y=f(x)$
in the square window defined by $-1\le x\le 1$ and $0\le y\le 2$. Also
plot the secant lines connecting $(0,f(0))$ and $(0+h,f(0+h))$ for
$h=.5$ and $h=.25$ in the same window. Give a table of values of the
slope of the secant lines connecting $(0,f(0))$ and
$\left(10^{-j},f\left(10^{-j}\right)\right)$ when $j$ is a positive
integer ranging from 1 to 5. What is an equation of the line tangent
to $y=3^x$ at $(0,1)$?

\medskip

\noindent b) Suppose $\displaystyle g(x)=6x\arctan\!\left({{\ln
x}\over{x^3+2}}\right)$. Plot $y=g(x)$ in the square window defined by
$0\le x\le 2$ and $-1\le y\le 1$. Also plot the secant lines
connecting $(1,g(1))$ and $(1+h,g(1+h))$ for $h=.5$ and $h=.25$ in the
same window.  Give a table of values of the slope of the secant lines
connecting $(1,g(1))$ and
$\left(1+10^{-j},g\left(1+10^{-j}\right)\right)$ when $j$ is a
positive integer ranging from 1 to 5. What is an equation of the line
tangent to $y=\displaystyle 6x\arctan\!\left({{\ln
x}\over{x^3+2}}\right)$ at $(1,0)$? 

\vfil\eject\end