Use Power Series Operations to Find the Taylor Series at X

question 438

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $\mathrm { x } ^ { 4 } \tan ^ { - 1 } ( 4 \mathrm { x } )$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { 2 n + 1 } x ^ { 2 n + 4 } } { 2 n + 1 }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 4 ^ { 2 n + 1 } x ^ { 2 n + 4 } } { 2 n + 1 }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 4 ^ { 2 n + 1 } x ^ { 2 n + 5 } } { 2 n + 1 }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \mathrm { n } } 4 ^ { 2 n + 1 } \mathrm { x } ^ { 2 \mathrm { n } + 5 } } { 2 \mathrm { n } + 1 }\)

---

Definitions:

Needy Families

Households that require financial assistance or social aid to meet their basic needs such as food, shelter, and healthcare.

Poverty Threshold

The minimum level of income deemed necessary to achieve an adequate standard of living in a specific geographical area.

Income Inequality

The uneven allocation of income among households or individuals within an economy.

World War II

A global conflict that took place between 1939 and 1945, involving most of the world's nations and resulting in significant geopolitical changes.