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AP® Calculus AB-BC

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Maclaurin Series as a Function $f(x)$

APCALC-JQM7GV

A function $f$ has the Maclaurin series given by:

$$2\left[ 1+\cfrac { { x }^{ 2 } }{ 2! } +\cfrac { { x }^{ 4 } }{ 4! } +\frac { { x }^{ 6 } }{ 6! } +....+\frac { { x }^{ 2n } }{ (2n)! } \right] $$

Which of the following is an expression for $f(x)$?

A

$\cos { x } $

B

${ e }^{ x }+\cos { x } $

C

${ e }^{ x }+{ e }^{ -x }$

D

$\cfrac { 1 }{ 2 } \left( { e }^{ x }+{ e }^{ -x } \right) $