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Solved: In Exercises 41–50, (a) find the series’ radius

University Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321717399 | Authors: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr. ISBN: 9780321717399 65

Solution for problem 42PE Chapter 9.PE

University Calculus: Early Transcendentals | 2nd Edition

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University Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321717399 | Authors: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr.

University Calculus: Early Transcendentals | 2nd Edition

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Problem 42PE

In Exercises 41–50, (a) find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) absolutely and (c) conditionally.

Step-by-Step Solution:
Step 1 of 3

Fourier Series The function, ex, is called the fundamental periodic function as it is a combination of sin mx and cos mx. A periodic function, f(x), over [−π,π] can be expanded by a linear combination of the fundamental periodic functions as ∞ ∑ imx f(x) = cme . (1) m=−∞ −inx Multiplying e on the both sides of eq.(1) and integrating the result from −π to π yields ∫ ∞ ∫ ▯ −inx ∑ ▯ i(m−n)x f(x)e dx = cm e dx (2) −▯ m=−∞ −▯

Step 2 of 3

Chapter 9.PE, Problem 42PE is Solved
Step 3 of 3

Textbook: University Calculus: Early Transcendentals
Edition: 2
Author: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr.
ISBN: 9780321717399

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Solved: In Exercises 41–50, (a) find the series’ radius