Find the Maclaurin Series for the Given Function $\sin 8 x$

question 158

Multiple Choice

Find the Maclaurin series for the given function.
- $\sin 8 x$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { 2 n + 1 } 8 ^ { 2 n + 1 } x ^ { 2 n + 1 } } { n ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 8 ^ { 2 n + 1 } x ^ { 2 n + 1 } } { n ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { 2 n + 1 } 8 ^ { 2 n + 1 } x ^ { 2 n + 1 } } { ( 2 n + 1 ) ! }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 8 ^ { 2 n + 1 } x ^ { 2 n + 1 } } { ( 2 n + 1 ) ! }\)

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Definitions:

Element

A substance that cannot be changed to a simpler substance by a normal chemical reaction.

Neutrons

Subatomic particles without an electric charge, found in the nucleus of an atom, contributing to the atom's mass.

Electrons

subatomic particles with a negative charge, found in all atoms and acting as the primary carrier of electricity in solids.

Valence Shells

The outermost electron shell of an atom that determines its bonding behavior with other atoms.