%% Math 131 Make-Up Midterm 1, Fall 2003

\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,epic,eepic}

\pagestyle{myheadings}
\markright{Math 131, Make-Up Midterm}

%% \setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\textheight}{8.5in}

\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{$\vphantom{\Big|}$}

\newcommand{\fahr}{{}^\circ\,\textrm{F}}

\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, Make-Up Midterm 1} \\
\textbf{Thursday, October 2, 6:30 PM} \\
Professor Hwang
\end{center}

\vfil

\noindent{\bf Name}: \Blank
\vskip 0pt plus .3fil

\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 \\
\hline
2       & \hfil/\  15\hfil \Strut \\
\hline
3 (a)   & \hfil/\  10\hfil \Strut \\
3 (b)   & \hfil/\  10\hfil \Strut \\
\hline
4       & \hfil/\  10\hfil \Strut \\
\hline
5       & \hfil/\  20\hfil \Strut \\
\hline
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 $\ds\lim_{x\to4}\frac{x^2-x-2}{x^2-5x+6}$
\vskip 0pt plus .5fil
\Answer{Answer}

\hrulefill

\item{(b)} [10 points]\quad $\ds\lim_{x\to2}\frac{x^2-x-2}{x^2-5x+6}$
\vskip 0pt plus .5fil
\Answer{Answer}

\ed

\hrulefill

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

\vfil

\eject

\item{} A population of bacteria triples every 90~minutes. 

\bd

\item{(a)} [10~points]\quad Find the doubling time of the population.

\vfil

\item{(b)} [10~points]\quad If one bacterium starts to grow at the
  rate above, how many hours pass until there are one billion
  ($10^9$)~bacteria?

\vfil

\Answer{Time until one billion bacteria}
\ed

\eject

\item{} [10~points]\quad One day in February at the White Mountain
  Field Station, the temperature varied sinusoidally between a low of
  $10\fahr$~at 5~AM and a high of $45\fahr$~at 5~PM. Write a formula
  for~$H$ as a function of~$t$, with $t$~measured in hours from 5~AM,
  and use your answer to estimate the temperature at 2~PM.
  You may use the graph below for reference.

\begin{center}
\input{makeup1a.eepic}
\end{center}

\vfil

\Answer{Temperature at 2~PM}

\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. The space shuttle's orbit
  has radius 4100~miles. Find the period of the orbit (in minutes) to
  the nearest minute.

  \vfil

\Answer{Period of space shuttle orbit}

\eject

\item{} An automobile costs \$18,000, and depreciates in value by
  17\%~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.
\vfil

\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.

\vfil

\Answer{Depreciation on first day}

\ed

\end{enumerate}

\end{document}

