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Get Full Access to University Calculus: Early Transcendentals - 2 Edition - Chapter 9.pe - Problem 42pe
Get Full Access to University Calculus: Early Transcendentals - 2 Edition - Chapter 9.pe - Problem 42pe

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# Solved: In Exercises 41–50, (a) find the series’ radius ISBN: 9780321717399 65

## Solution for problem 42PE Chapter 9.PE

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

Step 3 of 3

##### ISBN: 9780321717399

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