Use the definition to find the Taylor series (centered at c) for the function. $$f ( x ) = e ^ { 2 x } , c = 0$$
A) $\sum _ { n = 0 } ^ { \infty } \frac { 2 ^ { 2 n } } { n ! } x ^ { n }$
B)$\sum _ { n = 0 } ^ { \infty } \frac { 2 ^ { n } } { n ! } ( - 1 ) ^ { n } x ^ { n }$
C)$\sum _ { n = 0 } ^ { \infty } \frac { 2 ^ { n } } { n ! } x ^ { n }$
D)$\sum _ { n = 0 } ^ { \infty } \frac { 2 ^ { n } } { n ! } ( - 1 ) ^ { n } x ^ { 2 n }$
E)$\sum _ { n = 0 } ^ { \infty } \frac { 2 ^ { n } } { ( 2 n ) ! } x ^ { 2 n }$

Question

Quizplus · Accepted Answer

The Taylor series for $e^{2x}$ centered at $c=0$ is $\sum_{n=0}^{\infty} \frac{(2x)^n}{n!} = \sum_{n=0}^{\infty} \frac{2^n}{n!} x^n$.

Use the Definition to Find the Taylor Series (Centered at C)