Find the Maclaurin Series for F (X) Using the Definition $f ( x ) = x \cos ( 4 x )$

question 41

Multiple Choice

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

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 5 ^ { 2 n } x ^ { 2 n + 1 } } { ( 2 n ) ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 5 ^ { 2 n } x ^ { 2 n + 1 } } { n ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 5 ^ { 2 n } x ^ { 2 n + 1 } } { ( 2 n ) ! }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 5 ^ { n } x ^ { 2 n + 1 } } { ( 2 n ) ! }\)
• E) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 5 ^ { 2 n } x ^ { 2 n } } { ( 2 n ) ! }\)

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A statistical method used for hypothesis testing and constructing confidence intervals, especially useful when dealing with small sample sizes and unknown population standard deviations.

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