%% Math 131, Fall, 2003
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\begin{center}
\textbf{Holy Cross College, Fall Semester, 2003} \\
\textbf{Math 131, Professor Hwang} \\
Worksheet on Linear Approximation
\end{center}

\noindent The area and volume of a sphere of radius~$r$ are given by
\[
A=4\pi r^2,\qquad V=\frac{4}{3}\pi r^3.
\]
Use linear approximation to answer the following questions:

\be

\item If the radius is increased by~1\%, by about what percent does
  the area change?

\vfil

\item If the radius is increased by~5\%, by about what percent does
  the area change?

\vfil

\item If the radius is increased from $4$~cm to $4.2$~cm, by exactly
  how much does the area change? Is this consistent with your results
  above? 

\vfil

\hrulefill

\item If the radius is increased by~1\%, by about what percent does
  the volume change?

\vfil

\item If the radius is increased by~4\%, by about what percent does
  the volume change?

\vfil

\item If the radius is increased from $20$~cm to $20.8$~cm, by exactly
  how much does the volume change? Is this consistent with your
  results above?

\vfil

\hrulefill

\item If the volume is increased by~1\%, by about what percent does
  the area change?

\vfil

\item If the volume is increased by~3\%, by about what percent does
  the area change?

\vfil

\item Describe at least two different approaches to the last two
  questions. 

\ee

\eject

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