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Find the first three terms of the series for: e^x cosx

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.3: Arithmetic Sequences And Series

Problem 28E

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Question

Find the first three terms of the series for: e^x cosx

Expert Solution

Step 1

Sol:-

The series expansion of e^xcos(x) can be obtained by using the Taylor series expansion

$Taylor series of function f (x) at a is defined as : f (x) = f (0) + \frac{f^{'} (0)}{1!} (x - 0) + \frac{f^{''} (0)}{2!} {(x - 0)}^{2} + \frac{f^{'''} (0)}{3!} {(x - 0)}^{3} + \dots Find the derivatives of f (x) = e^{x} \cos (x)$

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