Math Problem Statement

The current i in a certain electric circuit is

iequals

8 sine pi t

.

Write the first three terms of the Taylor series of this function about

tequals

StartFraction 3 pi Over 2 EndFraction

.

Question content area bottom

Part 1

Choose the correct answer below.

A.8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 8 sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 8 sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

B.8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 pi cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 8 pi squared sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 pi cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 8 pi squared sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

C.8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 4 sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 4 sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

D.8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 pi cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 4 pi squared sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

8 sine StartFraction 3 pi squared Over 2 EndFraction plus 8 pi cosine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis minus 4 pi squared sine StartFraction 3 pi squared Over 2 EndFraction left parenthesis t minus StartFraction 3 pi Over 2 EndFraction right parenthesis squared plus midline ellipsis

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Taylor Series
Trigonometric Functions

Formulas

Taylor series formula: f(a) + f'(a)(x - a) + (f''(a)/2)(x - a)^2 + ...

Theorems

Taylor's theorem

Suitable Grade Level

Grades 11-12

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