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Single Variable Calculus

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Moderate

Multiplying Taylor Series

SVCALC-1P8QQV

Find the coefficient of $x^4$ in the Taylor series for:

$$f(x)=\frac{\cos x}{1-x} $$

...about $x=0$.

(Hint: although the problem can be done directly, consider using the theorem that states that Taylor series can be multiplied.)

A

$-\cfrac{1}{4}$

B

$-\cfrac{1}{24}$

C

$\cfrac{13}{24}$

D

$\cfrac{23}{24}$

E

$\cfrac{5}{2}$