Find the Power Series for the Function $f ( x ) = e ^ { x ^ { 8 } }$

question 37

Multiple Choice

Find the power series for the function $f ( x ) = e ^ { x ^ { 8 } }$ using the power series for $e ^ { x }$ .

• A) \(\sum _ { n = 1 } ^ { \infty } \frac { x ^ { 8 ( n + 1 ) } } { ( n + 1 ) ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 8 n } } { n ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 8 ( n + 1 ) } } { ( n + 1 ) ! }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 8 n } } { ( n + 1 ) ! }\)
• E) \(\sum _ { n = 1 } ^ { \infty } \frac { x ^ { 8 ( n + 1 ) } } { n ! }\)

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