\documentclass[addpoints,12pt]{exam} % can add 'answers' option
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\newcommand{\dueday}{Friday}
\newcommand{\duewhen}{12/6/19 at 11:59pm}
\newcommand{\hwnum}{9}
\newcommand{\classnumber}{Math 20C -- Swanson }
\newcommand{\classiteration}{Fall 2019}

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{Due \duewhen}
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\begin{document}
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  \classnumber -- \classiteration \\
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\begin{itemize}
  \item The graded part of the homework is on WebAssign.
  \item The problems below are also assigned and you are responsible for doing them,
    but they will not be collected or graded.
\end{itemize}

\newpage

\begin{questions}
  \question Consider the rectangle $R = [1, 3] \times [4, 5]$ in the $xy$ plane.
    A 3D object $E$ lies above the rectangle $R$ and below $z=y+2$.
    The units for $x, y, z$ are cm. Include units in your answers.
    The density at $(x, y, z)$ is $\rho(x, y, z) = e^x\, \text{g}/\text{cm}^3$.
    \begin{enumerate}[(a)]
      \item Compute the volume of $E$ using
        \[ \text{Volume} = \iint_R ((z\text{ at top}) - (z\text{ at bottom}))\,dA. \]
      \item Compute the mass of $E$ using
        \[ \text{Mass} = \iiint_E \rho(x, y, z)\,dV
            = \iint_D \int_{\text{$z$ at bottom}}^{\text{$z$ at top}}
               \rho(x, y, z)\,dz\,dA = \cdots. \]
      \item Compute the average density of $E$:
        \[ \text{Average of $\rho(x, y, z)$ over $E$} = \frac{\text{Mass of $E$}}{\text{Volume of $E$}} \]
    \end{enumerate}
    
    \begin{solution}
      
    \end{solution}
    \newpage
\end{questions}
\end{document}