Use Power Series Operations to Find the Taylor Series at X

question 409

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $x ^ { 5 } e ^ { 4 x }$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { 4 ^ { n + 5 } x ^ { n + 5 } } { ( n + 5 ) ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { 4 ^ { n _ { x ^ { n } } + 5 } } { ( \mathrm { n } + 5 ) ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { 4 ^ { n _ { x } } { } ^ { n + 5 } } { n ! }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { 4 ^ { n + 5 } x ^ { n + 5 } } { n ! }\)