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\LARGE 

{\hspace{50mm}Quiz 7
\hspace{50mm}Name:\hspace{20mm}}


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Directions:  Answer each question to the best of your ability.  You may use a calculator, but you must show all work to receive full credit.
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\begin{enumerate}
\item For each of the geometric series, find $a$ and $r$, and state the infinite sum.  (3 pts each)
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\begin{enumerate}
\item $S=5+\frac{10}{3}+\frac{20}{9}+\frac{40}{27}+....$
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\item  $S=7-\frac{35}{6}+\frac{175}{36}-\frac{875}{216}+....$
\end{enumerate}

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\item Jack and Jill both deposit \$1000 into an investment account each month on the first of the month.  Jack is not very investment savvy, and despite having portfolio that loses 5\% each month, he continues to invest his \$1000 each month for a whole year.  Jill, on the other hand, is quite smart with her investments, and her portfolio increase by 2\% each month.  At the end of a year, how much more money does Jill have than Jack?  (6 pts)
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\item State the general formula to find the degree 3 Taylor polynomial around $x=a$.  (3 pts)
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\item Find the degree 3 Taylor polynomial for the following functions around the given value of $a$ (4 pts each)
\begin{enumerate}
\item $f(x)= \ln x$, $a=1$
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\item $f(x)=\frac{1}{ \sqrt[3]{(1+x)^2} }$, $a=0$
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\end{enumerate}

\item Given you answer to 4.(a), estimate the value of $\ln 1.1$. (2 pts)
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\end{enumerate}

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