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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Definitions:

Relationship

The manner in which two or more ideas, items, or individuals are linked, or the condition of being linked.

Variable

An attribute, characteristic, or measurement that can take on different values across individuals, objects, or time points in data collection and analysis.

Increases

A term indicating a rise or growth in a numerical value or quantity.

Scatter Diagram

A graph used in statistics to visually display and analyze the relationship between two numerical variables by plotting data points on a Cartesian plane.