Use Power Series Operations to Find the Taylor Series at X

question 91

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $$x ^ { 8 } e ^ { x }$$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { 8 ^ { n _ { x ^ { n } } } } { n ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { n + 8 } } { n ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { 8 ^ { n _ { x } n } } { ( n + 8 ) ! }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { n + 8 } } { ( n + 8 ) ! }\)

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Definitions:

Care

The provision of what is necessary for the health, welfare, maintenance, and protection of someone or something.

Adult Children

Adults who maintain a child-like dependency on their parents or parental figures, often due to emotional or economic reasons.

Aging Parents

The phenomenon of adult children coping with and caring for their elderly parents, including the challenges that arise.

Sense of Attachment

The emotional bond that forms between individuals, particularly seen in relationships such as between parent and child.