Answered: Periodically extend and determine the…

Periodically extend and determine the Fourier series (I) and Use the Fourier series of the function f to obtain a series expression (II)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Question

Periodically extend and determine the Fourier series (I) and Use the Fourier series of the function f to obtain a series expression (II)

(1)
f(t) =
if - T≤t <0
0, if
t², if 0 < t <T

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Step 1: Introduction

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Step 2: Expanding f periodically and calculating a_0

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Step 3: Calculating Fourier coefficient a_n

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Step 4: Calculating Fourier coefficient b_n

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Step 5: Calculating Fourier series

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