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

question 9

Multiple Choice

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

• A) \(e ^ { 12 } \sum _ { n = 0 } ^ { \infty } \frac { ( x ) ^ { n } } { n ! }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { ( x - 12 ) ^ { n } } { ( n + 1 ) ! }\)
• C) \(e ^ { 12 } \sum _ { n = 0 } ^ { \infty } \frac { ( x - 12 ) ^ { n } } { n ! }\)
• D) \(e ^ { 12 } \sum _ { n = 0 } ^ { \infty } \frac { ( x ) ^ { n + 1 } } { ( n + 1 ) ! }\)
• E) \(\sum _ { n = 0 } ^ { \infty } \frac { ( x - 12 ) ^ { 2 n } } { 2 n ! }\)

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