By multiplying the Taylor series for e and sin x, find the terms through x³ of the Taylor series for e'sin x. This series is the imagi- nary part of the series for e* • eix = e(1+i}x_ Use this fact to check your answer. For what values of x should the series for e'sin x converge?

By multiplying the Taylor series for e and sin x, find the terms through x³ of the Taylor series for e'sin x. This series is the imagi- nary part of the series for e* • eix = e(1+i}x_ Use this fact to check your answer. For what values of x should the series for e'sin x converge?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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Question

Sequences and Series

By multiplying the Taylor series for e" and sin x, find the terms
through x of the Taylor series for e*sin x. This series is the imagi-
nary part of the series for
e* . eir = e(l+i)x_
Use this fact to check your answer. For what values of x should the
series for e"sin x converge?

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