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AP® Calculus AB-BC

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The Degree of a Series Expansion

APCALC-YLZJLE

Consider the function:

$$f(x) = e^x-e^{-x}-2\sin x-\cfrac{2x^3}{3}$$

Find the least value of $n$ for which: $\cfrac{d^n}{dx^n}f(x)$ at $x=0 $ is non-zero.

A

$1$

B

$2$

C

$5$

D

$7$