Use Power Series Operations to Find the Taylor Series at X

question 394

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $\cos ^ { 2 } ( 2 x )$

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

---

Definitions:

Customer Messages

Communication from a business to its customers, tailored to meet their needs and inquiries.

Self-Employed

A status where an individual works for themselves, rather than an employer, and is responsible for their own business.

Social Media Space

Refers to the digital environment where users engage, share, and interact with content on platforms like Facebook, Twitter, and Instagram.

Side Hustle

Any type of employment undertaken in addition to one's full-time job, typically freelance or piecework, to supplement income.