\input epsf
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\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $f(x)=\sqrt{3x+6x^4}$.

\medskip

\noindent a) Prove that $f$ is increasing on the interval $[0,1]$.

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\noindent b) Write down a finite sum which will be within $10^{-10}$
of the true value of the area enclosed by the $x$-axis, $y=f(x)$, and
$x=1$. You are {\it not} asked to actually compute the sum, just
describe it in any convenient fashion.

\medskip

\noindent {\bf Hint} Your reasoning and your explanation may be guided by the
picture below. Note that the horizontal and vertical axes have
different scales. The shaded rectangles represent the difference
between right- and left-endpoint approximations.

\medskip 

\centerline{\epsfbox{w7G.eps}}

\vfil\eject\end

