Math 152                                                                                         Name:
Quiz 4
  1. Find the Taylor series for $f(x)=\sin x$ centered at $a=\dfrac{\pi }{6}.$(Show at least 5 non-zero terms in your term-by-term series. Do not try to use Sigma notation.)

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  2. Find (or state) the Maclaurin series for each of the following. You may write your series out term-by-term or use sigma notation.
    1. $\cos x$

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    2. MATH

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    3. MATH

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    4. MATH

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  3. Use the first 3 terms of the series expansion for $e^{x}$ to estimate $e^{0.1}.$ Simplify your answer as much as possible.