Apply Taylor's Theorem to Find the Power Series Centered At c

question 75

Multiple Choice

Apply Taylor's Theorem to find the power series centered at $c = 0$ for the function $f ( x ) = e ^ { 12 x }$ .

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { ( n + 1 ) ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n } } { ( n + 1 ) ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n } } { n ! }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { n ! }\)
• E) \(\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { n ! }\)

---

Definitions:

Groupthink

A mental process in which the pursuit of agreement or uniformity among group members leads to illogical or ineffective conclusions in decision making.

Social Interference

The impact of social factors or interactions that disrupt or modify an individual's behavior or mental processes.

Groupthink

A psychological phenomenon that occurs within a group of people, where the desire for harmony or conformity results in an irrational or dysfunctional decision-making outcome.

Censoring

The suppression or prohibition of any parts of books, films, news, etc. that are considered obscene, politically unacceptable, or a threat to security.