\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose
$f(x)=x^{\vphantom{j_{J_{J_{J_J}J}}}\left(\!{1\over 10}\!\right)}$,
$g(x)=e^{\vphantom{j_{J_{J_{J_J}J}}}\left(\!{x \over 100}\!\right)}$,
and $h(x)=\ln x$.

\medskip

\noindent a) Find an interval of positive numbers where the graph of
$f$ is above the graph of both $g$ and $h$.

%[2,3] for example.

\medskip

\noindent b) Find an interval of positive numbers where the graph of
$g$ is above the graph of both $f$ and $h$.

%[5000,6000] for example. 

\medskip

\noindent c) Find an interval of positive numbers where the graph of
$h$ is above the graph of both $f$ and $g$.

%[1000,2000] for example.

\medskip

\noindent d) Suppose we consider a very short interval of positive
numbers very close to 0, such as $\left[10^{-10},2\cdot
10^{-10}\right]$. Which graph will be on top? Which graph will be on
the bottom?

\medskip

\noindent e) Suppose we consider an interval of positive numbers which
are very large, such as $\left[10^{100},2\cdot 10^{100}\right]$.
Which graph will be on top? Which graph will be on the bottom?


\vfil\eject\end

