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\pagestyle{myheadings}
\def\la{\langle}  \def\ra{\rangle}
\def\header{{\hfill Exam 2 Conflict\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
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\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 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}   13.1-9
\par Let $V$ be the volume of the solid that lies under the graph
of $f(x,y)=\sqrt{52-x^2-y^2}$ and above the rectangle given
by $2\leq x\leq 4, \; 2\leq y\leq 6$.  For the partition $R$ defined
by the lines $x=3$ and $y=4$, let $L$ and $U$ be the Riemann sums computed
using lower left corners and upper right corners, respectively.
Without calculating the numbers $V,L,$ and $U$, arrange them in
increasing order and explain your reasoning.


\prob{14}   13.2-23
\par Sketch the volume of the solid whose volume is given by the iterated
integral
$\int_0^1\int_0^1\;(4-x-2y)\;dxdy$.

\prob{14}   13.3-37
\par Sketch the region of integration and change the order of
integration.
$$\int_0^4\int_{y/2}^2\; f(x,y)dxdy$$


\prob{14}  13.4-21
\par Use polar coordinates to find the volume of the solid
inside both the cylinder
$x^2+y^2=4$ and the ellipsoid  $4x^2+4y^2+z^2=64$.

\prob{14}  13.5-11
\par Find the mass of the lamina (a thin plate) that
occupies the region
 $$D=\{(x,y)|\; 0\leq y\leq \sin x,\; 0\leq x\leq \pi\}$$
and has a density function $\rho(x,y)=y$.

\prob{14}   13.7-13
\par Evaluate the triple integral $\int\int\int_E z dV$ where $E$ is
the three dimensional solid
bounded by the planes $x=0$, $y=0$, $z=0$, $y+z=1$, and $x+z=1$.

\prob{8}   14.1-3
\par Sketch the vector field ${\bf F}(x,y)=y\i\;+\;\j$.

\prob{12}   14.2-37
\par Find the work done by the force field
$${\bf F}(x,y,z)=xz\i+yx\j+zy\k$$ on a particle that moves along
the curve ${\bf r}(t)=t^2\i-t^3\j+t^4\k,\;\; 0\leq t\leq 1$.

\finishtbl
%\printanswers

\end{document}