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\begin{center} Quiz 4, Calculus 2
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\textbf{Name:} \underline{\hspace{3in}}

\begin{enumerate}
\item (4 points) A trough has the shape of a triangular prism, with the pointy end down.  The triangle is isosceles, with a base of 3 feet and height of 6 feet.  The trough is 10 feet long.  Suppose that the trough is only filled up to \underline{half} of its depth with water.  Set up, but \tb{do not integrate} an integral that represents how much work is needed to pump out all of the water over the side of the trough.  As usual, the density of water is 62.5 lbs/ft$^3$.

\newpage 

\item (2 points) Determine if the sequence $\d a_n=\frac{\cos^2 n}{2^n}$ converges or diverges.  If it converges, find the limit.  Make sure to \underline{explain your reasoning}.
\vspace{3in}

\item (4 points)  Determine if the series is convergent or divergent.  If it converges, find the limit.  Make sure to \underline{explain your reasoning}.
\begin{enumerate}
	\item $1 + \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\cdots$
	\vspace{2in}
	\item $\d\sum^{\infty}_{n=0} \frac{3^{n+1}}{\pi^n}$
\end{enumerate}

\end{enumerate}
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