Find the Maclaurin Series for the Function $f ( x ) = \cos \left( 2 x ^ { 2 } \right)$

Find the Maclaurin series for the function $f ( x ) = \cos \left( 2 x ^ { 2 } \right)$ , and give the interval of convergence of the series.

A) $\sum _ { k = 0 } ^ { \infty } \frac { 2 ^ { 2 k } } { ( 2 k ) ! } x ^ { 2 k }$ interval of convergence: (-?, ?)
B) $\sum _ { k = 0 } ^ { \infty } \frac { 2 ^ { 2 k } } { ( 2 k ) ! } x ^ { 2 k }$ interval of convergence: (0, 1)
C) $\sum _ { k = 0 } ^ { \infty } \frac { ( - 1 ) ^ { k } 2 ^ { 2 k } } { ( 2 k ) ! } x ^ { 2 k }$ interval of convergence: (-?, ?)
D) $\sum _ { k = 0 } ^ { \infty } \frac { ( - 1 ) ^ { k } 2 ^ { 2 k } } { ( 2 k ) ! } x ^ { 4 k }$ interval of convergence: (-?, ?)