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\textbf{Math 220 \hfill Quiz 12 (take-home) \hfill Spring 2014} \\
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\noindent
\textbf{Name}\ \rule{3.5in}{.4pt}
\noindent
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\begin{center}
(circle your TA discussion section)
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\vspace{0.03in}
\begin{small}
\begin{tabular}{lllll}
$\triangleright$ & \textbf{AD1}, TR 9:00-10:50, Darlayne Addabbo & \hspace{0.2in} & $\triangleright$ & \textbf{ADH}, TR 3:00-3:50, Paulina Koutsaki \\
$\triangleright$ & \textbf{AD2}, TR 1:00-2:50, Ben Fulan & \hspace{0.2in} & $\triangleright$ & \textbf{ADJ}, TR 9:00-9:50, Jed Chou \\
$\triangleright$ & \textbf{ADA}, TR 8:00-8:50, Chris Bailey & \hspace{0.2in} & $\triangleright$ & \textbf{ADK}, TR 10:00-10:50, Jed Chou \\
$\triangleright$ & \textbf{ADB}, TR 9:00-9:50, Chris Bailey & \hspace{0.2in} & $\triangleright$ & \textbf{ADL}, TR 11:00-11:50, Andrew McConvey \\
$\triangleright$ & \textbf{ADC}, TR 10:00-10:50, Andrew McConvey & \hspace{0.2in} & $\triangleright$ & \textbf{ADM}, TR 12:00-12:50, Benjamin Wright \\
$\triangleright$ & \textbf{ADD}, TR 11:00-11:50, Diaa Taha & \hspace{0.2in} & $\triangleright$ & \textbf{ADN}, TR 1:00-1:50, Benjamin Wright \\
$\triangleright$ & \textbf{ADE}, TR 12:00-12:50, Paul Spiegelhalter & \hspace{0.2in} & $\triangleright$ & \textbf{ADO}, TR 2:00-2:50, Paul Spiegelhalter \\
$\triangleright$ & \textbf{ADF}, TR 1:00-1:50, Diaa Taha & \hspace{0.2in} & $\triangleright$ & \textbf{ADP}, TR 3:00-3:50, Wan-Yu Wu \\
$\triangleright$ & \textbf{ADG}, TR 2:00-2:50, Paulina Koutsaki & \hspace{0.2in} & $\triangleright$ & \textbf{ADQ}, TR 4:00-4:50, Wan-Yu Wu \\
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\begin{itemize}
\item You may work with other MATH 220 students. However each student should write up solutions separately and independently -- nobody should copy someone else's work.
\item You may use your notes, the textbook, or information found on my course home page.
\item The only computational technology you may use is the basic arithmetic features of a calculator for problem 3.
\item You are not allowed to search the Internet, use Wolfram Alpha, or use technology for anything beyond what is stated above.
\item The quiz should be submitted to Mr. Murphy at the beginning of your official lecture period on Friday, April 25th.
\item There is a higher expectation for the quality of your work on a take-home quiz. Everything should be written logically and legibly with sufficient work to justify each answer. Blank copies of the quiz are available on the course home page.
\item Be sure that the pages are nicely stapled -- do not just fold the corners.
\item \textbf{Note to TAs and Tutors -- you should not help students with these specific problems or go over solutions until after 5pm Friday.}
\end{itemize}
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\begin{enumerate}
\item (3 points) Use the techniques of linear approximation found in section 3.10 to obtain a good estimate for $\D{\left( 122 \right)^{2/3}}$ without the use of technology. Simplify and write your answer in decimal form.
\vspace{5in}
\item (3 points) Suppose that the polynomial $g(x)$ is an odd function and satisfies the following conditions.
\begin{itemize}
\item $\D{g(3) = 7}$
\item $\D{g'(3) = 4}$
\item $\D{g''(3) = 3}$
\item $\D{g'''(3) = 2}$
\end{itemize}
Use the techniques of linear approximation found in section 3.10 to estimate the value of $g(-3.2)$. Simplify and write your answer in decimal form.
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\item (4 points) There is one value of $x$ for which the line tangent to the graph of $\D{f(x) = x^4 + x^2}$ is perpendicular to the line $\D{y = \tfrac{1}{20}x - 10}$. Determine this $x$-value using Newton's Method with an initial estimate of $x_1 = -1$. You should use this method 3 times in order to obtain estimates $x_2$, $x_3$ and $x_4$. You are only allowed to use technology for basic arithmetic. Your final answer should include 5 places after the decimal point.
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\end{enumerate}
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