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\textbf{Math 220 \hfill Quiz 7 (take-home) \hfill Fall 2010} \\
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\textbf{Your Name}\ \rule{3.5in}{.4pt} \hfill \\[0.3in]
\textbf{TA's Name}\ \rule{3.5in}{.4pt} \hfill \\[0.3in]
\textbf{Discussion Section}\ \rule{3.5in}{.4pt} \hfill \\ \hspace*{0.3in} \textrm{\small (list either section number or meeting times)} \\[0.3in]
\begin{itemize}
\item You may work with other students in this class. However each student should write up solutions separately and independently -- nobody should copy someone else's work.
\item You may use your notes or the textbook.
\item No calculators or computers are allowed on any problem.
\item You must show sufficient work to justify each answer.
\item The quiz should be turned in to your TA at the beginning of your discussion section meeting on Monday, October 11 (Merit sections) or Tuesday, October 12 (other sections).
\item Be sure that the pages are nicely stapled -- do not just fold the corners.
\item Note to TA's -- you should not help students with these specific problems or go over solutions until after 4pm Tuesday.
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\item (3 points) Find the equation of the line tangent to the curve given by $\D{x^2 + 6xy^2 + y^3 = 17}$ at the point $(2,1)$.
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\item (2 points) For the given function, use logarithmic differentiation to find a formula for $\frac{dy}{dx}$ written in terms of $x$.
$$y = \left(x^5 + 1\right)^{3x^2}$$
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\item (2 points) Given that $\D{\frac{dw}{dr} = 0.25w}$ and $\D{w(4)=3}$, find a formula for $w$ as a function of $r$.
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\item (3 points) A ball is thrown straight up from an initial height of $8$ feet above the ground. Until the ball hits the ground, the function $h = -16\left(t-\frac{1}{2}\right)^2 + 12$ represents the ball's height in feet above ground level $t$ seconds after it was thrown. What is the velocity of the ball when it hits the ground?
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