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\textbf{Math 220 \hfill Quiz 7 (take-home) \hfill Spring 2010} \\
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\textbf{Name}\ \rule{3.5in}{.4pt} \hfill \\[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 and the textbook.
\item You should not use a calculator except to do basic arithmetic.
\item Show sufficient work to justify each answer.
\item There is no specific time limit, but the quiz is due at the beginning of Tuesday's discussion section (Monday for Merit sections).
\item Note to TA's -- you should not help students with these specific problems or go over solutions until the last discussion section has turned in the quiz at 3pm Tuesday.
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\begin{enumerate}
\item (2 points) Find a formula for the derivative $\D{\frac{dy}{dx}}$ given that $\D{x^2 + 4xy +y^2 = 13}$. It is acceptable to leave your answer in terms of both $x$ and $y$.
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\item (2 points) Determine a formula for the line which is tangent to the graph of $\D{y = \tan^{-1}{\left(e^{6x}\right)}}$ at its $y$-intercept.
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\item (2 points) Find a formula for $f'(x)$ given that $\D{f(x) = \ln{\left(x^5e^{x^3}\left(x^4+3\right)^{6}\right)}}$.
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\item (4 points) Suppose that $t$ seconds after an object is shot directly upwards from the surface of some planet its height in feet is given by $\D{h=200t-2.5t^2}$.
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\item Find a formula for the velocity of the bullet at time $t$.
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\item What is the maximum height attained by the bullet?
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