Apply Taylor's Theorem to Find the Power Series Centered At c

question 75

Multiple Choice

Apply Taylor's Theorem to find the power series centered at $c = 0$ for the function $f ( x ) = e ^ { 12 x }$ .

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { ( n + 1 ) ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n } } { ( n + 1 ) ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n } } { n ! }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { n ! }\)
• E) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { n ! }\)