\input epsf
\nopagenumbers
\magnification=\magstep1

%{Note}\/ that the default location for four of the graphs is on the
%next page. 

\rightline{\epsfxsize=2.in \epsfbox{w6L0.eps}}

\vskip -2.in

\vtop{\hsize=3.2in \noindent {\bf Problem statement} Suppose $f$ is
defined by $f(x)= 3e^{\cos x}$. {\tt Maple} produced graphs of $f$ and
its first four derivatives on the interval $[2,7]$ (be careful when
examining the derivative graphs -- look carefully at the vertical
scales!). The graph of $f$ is to the right, and the graphs of the
first four derivatives of $f$ are on the back of this page. You should
assume that the graphs are correct for this problem.


\noindent Suppose $I$ is the value of $\displaystyle \int_2^7
f(x)\,dx$.

\medskip

\noindent a) Use the graph of $f$ alone to estimate $I$.
}
\medskip

\noindent b) Use the information in the graphs to tell how many
subdivisions $N$ are needed so that the Trapezoid Rule approximation
$T_N$ will approximate $I$ with error $< 10^{-5}$.

\medskip

\noindent c) Use the information in the graphs to tell how many
subdivisions $N$ are needed so that the Simpson's Rule approximation
$S_N$ will approximate $I$ with error $< 10^{-5}$.

\vfil\eject\vfil

\centerline{\epsfxsize=2.3in\epsfbox{w6L1.eps}\qquad \epsfxsize=2.3in
\epsfbox{w6L2.eps}}

\centerline{{\bf Graph of $f'$}\hskip 1.75in {\bf Graph of $f''$}}

\bigskip

\centerline{\epsfxsize=2.3in\epsfbox{w6L3.eps}\qquad \epsfxsize=2.3in
\epsfbox{w6L4.eps}}

\centerline{{\bf Graph of $f^{(3)}$}\hskip 1.75in {\bf Graph of $f^{(4)}$}}

\vfil\eject\end