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\def\header{{\hfill Exam 3 \hfill A. Miller \hfill Fall 2001
                                       \hfill Math 213\hfill}}
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\begin{document}

\bigskip

Show all work.  Circle your answer.

No books, no notes, no calculator, no cell phones, no pagers, no
electronic devices at all.

Solutions will be posted shortly after the exam:
www.math.wisc.edu/$\sim$miller/m213

\par\vskip .25in
\begin{center}
Name\makebox[3in]{\hrulefill} \\
\end{center}

\begin{center}
{\bf Circle your DIScussion section (column one):} \\
\end{center}

TA: Youngsuk Lee

\begin{center}
\begin{tabular}{l|l|l}
 DIS 301 & 8:50  T   & 6322 SOC SCI   \\
 DIS 302 & 8:50  R   & 215 INGRAHAM   \\
 DIS 303 & 9:55  T   & 225 INGRAHAM   \\
 DIS 304 & 9:55  R   & 495 VAN HISE   \\
\end{tabular}
\end{center}

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%\bigskip

\begin{center} \Large
 \begin{tabular}{||c|c|c||} \hline\hline
  Problem & Points & Score \\  \hline\hline
  \input{exam.tbl}
  \hline \hline
 \end{tabular}
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\prob{8} % 10.1 sep of var #12
Find the particular solution for the following equation and explicitly solve
for $y$.
 $${dy\over dx}=(x+2)^2e^y;\;\;\;\; y=0 \mbox{ when } x=1$$
\answer $y=-\ln(10-{{(x+2)}^3\over 3})$


\prob{7} % 10.4 applic #6
When Michael was born his grandfather deposited \$5000 into an account
for him earning 10\% annual interest compounded continuously.  His
grandfather also plans to deposit continuously an additional \$1000
per year.  How much will Michael have in his account when he is 20?

\answer $15000e^{2}-10000$

\prob{7} % 9.6  Double integration #50
Evaluate the double integral below.  If the function seems too difficult
to integrate, try interchanging the limits of integration.
$$\int_0^2 \int_{y/2}^1\;e^{x^2}\;dx\; dy$$
\answer $\int_0^1\int_0^{2x} e^{x^2}dydx=
\int_0^1{2x} e^{x^2}dx=e-1$

\prob{7} % 12.1 geometric series #40
An oil well produced \$1,000,000 of income its first year.  Each year
thereafter, the well produced half as much income as the previous year.
What is the total amount of income produced by the well in 20 years?
\answer \$2,000,000$(1-{1\over 2^{20}})$

\prob{7} % 9.5 total differentials #1
Use the total differential to approximate the quantity
$$\sqrt{(3.01)^2+(4.02)^2}$$
\answer $5.022$


\prob{7} % 9.4 Lagrange #28
A rectangular box with a square bottom and no top is to be built from $1200$
square inches of material. Find the dimensions that will enclose the maximum
volume.

\answer $20 \times 20 \times 10$

\prob{7} % 10.2 linear diff eq # 12
Find the all solutions of the differential equation:
$$x{dy\over dx}=2xy+x^2e^{3x}$$
\answer $y=e^{2x}((x-1)e^x+C)$


\finishtbl
\printanswers

\end{document}




