\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Consider the following sequences:
$$ a_n = \left(\! 1 + {1 \over n}\!\right)^{\! n}\,;\quad 
   b_n = \left(\! 1 + {1 \over {n^2}}\!\right)^{\! n}\,;\quad 
   c_n = \left(\! 1 + {1 \over {\sqrt n}}\!\right)^{\! n}\,. $$
\noindent a) Use your calculator to plot the first ten terms
of each of these sequences.  Then use this
information to guess the limiting behavior of each of the sequences. 

\medskip

\noindent b) Replace $n$ by $x$ and use L'Hopital's Rule to find the
limit of each as $x$ tends to infinity.

\vfil\eject\end

