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AP® Calculus AB-BC

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Moderate

3rd Non-Zero Term of Taylor Series of $\sin x$

APCALC-GIKLWZ

Which of the following is the $3^{rd}$ nonzero term in the Taylor series for $f(x) = \sin x$ centered at $x = π$?

A

$\cfrac{( x-\pi ) ^{ 5 }}{5!}$

B

$-\cfrac{( x-\pi ) ^{ 5 }}{5!}$

C

$\cfrac{(x-\pi)^3}{3!}$

D

$-\cfrac{(x-\pi)^3}{3!}$

E

$\cfrac{( x-\pi ) ^{ 7 }}{7!}$