By multiplying the Taylor series for ex and sin x, find the terms through x5 of the Taylor series for ex sin x. This series is the imaginary part of the series for ex . eix = e(1+i)x. Use this fact to check your answer. For what values of x should the series for ex sin x converge?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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By multiplying the Taylor series for ex and sin x, find the terms
through x5 of the Taylor series for ex sin x. This series is the imaginary
part of the series for
ex . eix = e(1+i)x.
Use this fact to check your answer. For what values of x should the
series for ex sin x converge?

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