Use the Definition to Find the Taylor Series Centered At c

question 26

Multiple Choice

Use the definition to find the Taylor series centered at
$c = 0 \text { for the function }$ $f ( x ) = 3 \ln \left( x ^ { 2 } + 1 \right)$

• A)\(3 \ln \left( x ^ { 2 } + 1 \right) = \sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { 2 n + 2 } } { n + 1 }\)
• B)\(3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { n + 1 } } { n + 1 }\)
• C)\(3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 2 n + 2 } } { n + 1 }\)
• D)\(3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 2 } } { n }\)
• E)\(3 \ln \left( x ^ { 2 } + 1 \right) = \sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { n + 1 } } { n + 1 }\)

---

Definitions:

Learned Inhibitions

Behaviors learned through experience that prevent an individual from engaging in certain actions.

Alcohol

A psychoactive substance commonly found in beverages such as beer, wine, and spirits, and known for its depressant effects.

Females Abuse

Females Abuse refers to the maltreatment or violent behavior directed towards females, encompassing physical, sexual, emotional abuse, and exploitation.

Nicotine

A potent parasympathomimetic alkaloid found in the nightshade family of plants that acts as a stimulant in small doses.