%% Math 131-01 Midterm, Fall 2003

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\markright{Math 131-03, Midterm}

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\def\Answer#1{$\phantom{.}$\hfill
	#1\quad\fbox{$\phantom{\Big|Put answer here}$}}
\def\Blank{$\underline{\phantom{Please write your name in this
	space}}$} 
\def\Strut{$\vphantom{\Big|}$}

\def\bd{\begin{description}}
\def\ed{\end{description}}
\def\ds{\displaystyle}

\begin{document}

\begin{center}

\textbf{Holy Cross College, Fall Semester, 2003} \\
\textbf{Math 131, Section 03, Midterm 1} \\
\textbf{Friday, September 26, Noon} \\
Professor Hwang
\end{center}

\vfil

\noindent{\bf Name}: \Blank
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\paragraph{Instructions} Please write your answers in the spaces
provided, and show work on the test itself. Use the back of the
preceding page if you need more space for scratch work.

\vfil

\noindent{\bf Please do not write in the space below}

\begin{center}
\begin{tabular}{|l||r|}
\hline
Problem & Points/Poss	 \Strut \\
\hline\hline
1 (a)	& \hfil/\ \ 5\hfil \Strut \\
1 (b)	& \hfil/\  10\hfil \Strut \\
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2	& \hfil/\  15\hfil \Strut \\
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3 (a)	& \hfil/\  10\hfil \Strut \\
3 (b)	& \hfil/\  10\hfil \Strut \\
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4	& \hfil/\  10\hfil \Strut \\
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5 	& \hfil/\  20\hfil \Strut \\
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6 (a)	& \hfil/\  10\hfil \Strut \\
6 (b)	& \hfil/\  10\hfil \Strut \\
\hline\hline
Total	& \hfil/100\hfil \Strut \\
\hline
\end{tabular}
\end{center}

\vfil\eject

\begin{enumerate}

\item{} Compute the following limits. 

\bd

\item{(a)} [5 points]\quad $\ds\lim_{x\to2}\frac{x^2-x-6}{x+2}$
\vskip 0pt plus .5fil
\Answer{Answer}

\hrulefill

\item{(b)} [10 points]\quad $\ds\lim_{x\to-2}\frac{x^2-x-6}{x+2}$
\vskip 0pt plus .5fil
\Answer{Answer}

\ed

\hrulefill

\item{}  [15 points]\quad Find the horizontal and vertical asymptotes
  of the function
\[
y=\frac{3x(x^2-3x+2)}{(x^2-1)(x+3)}
\]
Show all work, and clearly mark your answers.

\vfil

\eject

\item{} Barium-140 has a half-life of 12.75~days. 

\bd

\item{(a)} [10~points]\quad Find a formula $Q=Q_0e^{kt}$ for the
  amount of Barium-140 remaining after $t$~days.

\vfil

\item{(b)} [10~points]\quad How many days does it take for 99\%~of a
  sample of Barium-140 to decay? (Watch round-off error!)

\vfil

\Answer{99\% Decay Time}
\ed

\eject

\item{} [10~points]\quad The desert temperature~$H$ varies
  sinusoidally from a low of~$40^\circ\textrm{F}$ at 5~AM to a high
  of~$80^\circ\textrm{F}$ at 5~PM. Write a formula for~$H$ as a
  function of~$t$, with $t$~measured in hours from 5~AM. You may use
  the graph below for reference.

\begin{center}
\input{midterm1a.eepic}
\end{center}

\vfil

\eject

\item{} [20~points]\quad According to Kepler's law, the period of an
  earth satellite is proportional to the $\frac{3}{2}$~power of the
  radius of its orbit.  The moon's orbital period is 29~days, and the
  radius of its orbit is $238,000$~miles. Find the radius of the orbit
  of a satellite whose period is 24~hours.  \vfil

\Answer{Radius of Orbit (miles)}

\eject

\item{} An automobile costs \$20,000, and depreciates in value by
  20\%~per year.

\bd

\item{(a)} [10~points]\quad Compute the average rate of depreciation
  for the first year of ownership. Express your answer in dollars per
  day.
\vskip 0pt plus 0.5fil

\Answer{Average Depreciation (\$/day)}

\item{(b)} [10~points]\quad Estimate the actual depreciation for the
  first day of ownership. Express your answer in dollars, rounded to
  the nearest penny.

\vskip 0pt plus 0.5 fil

\Answer{Depreciation on first day}

\ed

\end{enumerate}

\end{document}

