% LaTex2e
\documentclass[12pt]{article}
\usepackage{amssymb,latexsym}

\def\i{{\;\bf i}}
\def\j{{\;\bf j}}
\def\k{{\;\bf k}}

\oddsidemargin 5pt \evensidemargin 5pt \marginparwidth 68pt
\marginparsep 10pt \topmargin 10pt \headheight 10pt
\headsep 15pt \footskip 35pt
\textheight = 625pt  \textwidth 440pt \columnsep 10pt \columnseprule 5pt

\pagestyle{myheadings}
\def\la{\langle}  \def\ra{\rangle}
\def\header{{\hfill Exam 2 \hfill A. Miller \hfill Fall 2000
                                       \hfill Math 234\hfill}}
\markboth\header\header
\newcount\probno
\newcount\total
\newwrite\examTBLFile

\probno=0
\def\prob#1{\advance\probno by 1  \vfill\newpage
%\def\prob#1{\advance\probno by 1 \par
    \noindent\the\probno . (#1 pts)\advance\total by #1
    \immediate\write\examTBLFile{\the\probno
       \string& #1 \string&
       \string\qquad \string\\ \string\hline}}

\def\probx#1{\advance\probno by 1  \vfill  % \par
    \noindent\the\probno . (#1 pts)\advance\total by #1
    \immediate\write\examTBLFile{\the\probno
       \string& #1 \string&
       \string\qquad \string\\ \string\hline}}

\def\finishtbl{
    \immediate\write\examTBLFile{Total \string& \the\total
    \string& \qquad \string\\ \string\hline}
     }

\newwrite\ans
\immediate\openout\ans=answers
\outer\def\answer{\par\medbreak
  \immediate\write\ans{}
  \immediate\write\ans{\string\bigskip \the\probno . }
  \copytoblankline}
\outer\def\putanswer{\par\medbreak
  \immediate\write\ans{}
  \copytoblankline}
\def\copytoblankline{\begingroup\setupcopy\copyans}
\def\setupcopy{\def\do##1{\catcode`##1=12}\dospecials
     \catcode`\|=12\obeylines}
{\obeylines \gdef\copyans#1
  {\def\next{#1}%
  \ifx\next\empty\let\next=\endgroup%
  \else\immediate\write\ans{\next}\let\next=\copyans\fi\next}}
\def\printanswers{\newpage\begin{center} Answers \end{center}
    \immediate\closeout\ans\input answers}

\begin{document}

\bigskip

\begin{quote}
{
No calculator, no cell phones, no pagers, no electronic devices at all.
\par You may bring in a single ``cheat sheet''.  One ordinary 8.5 x 11 sheet
of paper with anything you want written on both sides. } \end{quote}

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

\begin{center}
{\bf Hand in to your TA -- Circle your TA section:} \\
\end{center}
\begin{center}
\begin{tabular}{l|l|l}
DIS 321 & T 8:50    &  Milind Shah            \\
DIS 322 & R 8:50    &  Milind Shah            \\
DIS 323 & T 9:55    &  Milind Shah            \\
DIS 324 & R 9:55    &  Milind Shah            \\
DIS 325 & T 11:00   &  Duygu Unlu            \\
DIS 326 & R 11:00   &  Duygu Unlu            \\
DIS 327 & T 12:05p  &  Duygu Unlu            \\
DIS 328 & R 12:05p  &  Duygu Unlu            \\
DIS 329 & T 1:20p   &  Kiran Manchikanti     \\
DIS 330 & R 1:20p   &  Kiran Manchikanti     \\
DIS 331 & T 2:25p   &  Lipika Deka            \\
DIS 332 & R 2:25p   &  Lipika Deka            \\
DIS 333 & T 3:30p   &  Lipika Deka            \\
DIS 334 & R 3:30p   &  Lipika Deka            \\
\end{tabular}
\end{center}

% end file with \finishtbl
%\bigskip

\begin{center} \Large
 \begin{tabular}{||c|c|c||} \hline\hline
  Problem & Points & Score \\  \hline\hline
  \input{exam.tbl}
  \hline \hline
 \end{tabular}
\end{center}

\immediate\openout\examTBLFile=exam.tbl

\setcounter{page}{0}


\prob{10}  % 13.1-3
Calculate the double Riemann sum of $f$ for the partition of $R$ given
by the indicated lines and the given choice of $(x_{ij}^*,y_{ij}^*)$.
\par $f(x,y)=x^2+4y,\;\;\;\; R=\{(x,y)|\;\;0\leq x\leq 2,\;\;
1\leq y\leq 3\},$
\par $x=1,\; y=2;\;\;\;\;
(x_{ij}^*,y_{ij}^*)=$ upper right corner of $R_{ij}$.
\answer 50

\prob{14}  % 13.2-19
Calculate the double integral:
$$\int\int_R x\cos(x+y)\;dA,\;\;\;\;
R=[0,{\pi\over 2}]\times [0,{\pi}]$$
\answer $-2$


\prob{14}  % 13.3-41
Evaluate the integral by reversing the order of integration:
$$\int_0^2\int_{y^2}^4 y{e^{x^2}} dxdy $$
\answer ${1\over 4}(e^{16}-1)$


\prob{14}  % 13.4-27
Evaluate the integral by converting to polar coordinates:
$$\int_0^3\int_{-\sqrt{9-y^2}}^{\sqrt{9-y^2}} \;\; x^2y\;dxdy$$
\answer $162\over 5$

\prob{14}  % 13.5-9
Find the mass of the lamina (a thin plate) that occupies the region
$D$ and has a density function $\rho(x,y)=x$.  The region $D$ is bounded by
the parabola $x=y^2$ and the line $y=x-6$.
\answer $\int^3_{-2}\int^{y+6}_{y^2}\; x dxdy={250\over 3}$

\prob{14}  % 13.7-15
Evaluate the triple integral $\int\int\int_E (x^2+y^2)^2\; dV$ where $E$ is
the three dimensional solid
bounded by the paraboloid $z=x^2+y^2$ and the plane $z=4$.
\answer ${64\over 3}\pi$

\prob{8}  % 14.1-19
Find the gradient field ${\bf \nabla f}$ of $f(x,y)=e^{xy^2}$.
\answer ${\bf \nabla f}=y^2e^{xy^2}\i\;\;+\;\;2xye^{xy^2}\j$

\prob{12}  % 14.2-19
Evaluate the line integral $\int_C {\bf F}\cdot d{\bf r}$ where
$${\bf F}(x,y,z)=\sin(x)\i+\cos(y)\j+yz\k$$
$${\bf r}(t)=t\i+t^2\j+t^3\k\;\;\;\;\; 0\leq t\leq 1$$
\answer $\sin(1)-\cos(1)+{11\over 8}$

\finishtbl
\printanswers

\end{document}