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{\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. Each question is worth 5 points
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\begin{enumerate}
\item Find the first 4 non-zero terms of the Taylor series of $\sin x$ about $x=\pi$.
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\item Find the first 4 non-zero terms of the Taylor series of $\frac{1}{1-x^3}$ about $x=0$.
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\item Find the $n^{th}$ term of the Taylor series of $ \frac{d}{dx}e^{x^2}$ about $x=0$
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\item Find the error at $x=1$ on the first 4 non-zero terms of the Taylor series of $\sin x$ centered at $x=0$
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\item Determine the number of terms of the Taylor series for $f(x)$ necessary to approximate $ \sin 1$ to the nearest .0000000001.
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\end{enumerate}

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