Find the Maclaurin Series For $f ( x )$ Using the Definition of the Maclaurin Series

question 27

Multiple Choice

Find the Maclaurin series for $f ( x )$ using the definition of the Maclaurin series.
$$f ( x ) = x \cos ( 4 x )$$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { n } x ^ { 2 n + 1 } } { ( 2 n ) ! }\)
• B)
• \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { 2 n } x ^ { 2 n + 1 } } { n ! }\)
• C)
• \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { 2 n } x ^ { 2 n } } { ( 2 n ) ! }\)
• D)
• \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { 2 n } x ^ { 2 n + 1 } } { ( 2 n ) ! }\)
• E)
• \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 4 ^ { 2 n } x ^ { 2 n + 1 } } { ( 2 n ) ! }\)

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