Use the Definition to Find the Taylor Series Centered At c

question 145

Multiple Choice

Use the definition to find the Taylor series centered at $c = 0 \text { for the function }$ $f ( x ) = \sin 4 x$

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

---

Definitions:

Life Expectancy

The average period a person is expected to live, based on statistical averages of age, sex, and other factors in a given population.

Warning Sign

An indication or symptom that suggests the presence of a potential issue, problem, or danger that requires attention.

Extended Regression

A statistical technique that involves extending the regression analysis to include multiple independent variables and their interactions.

Depressive Disorder

A group of conditions characterized by persistent feelings of sadness, hopelessness, and a lack of interest or pleasure in activities, significantly affecting daily life.