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

question 103

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

---

Definitions:

Affective Commitment

The emotional attachment an employee feels towards their organization, which significantly influences their willingness to contribute to the organization's goals.

Socialization Practices

Methods and processes used to integrate newcomers into an organizational culture and acquaint them with their new roles.

Continuance Commitment

The level of commitment an individual feels to an organization based on the costs they perceive in leaving it.

Normative Commitment

An individual's psychological attachment to an organization, characterized by a feeling of obligation to remain with the organization.