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Problem 1. Find the Fourier cosine series for the function f(x) = T – x, 0 < x < T. %3D

Problem 1. Find the Fourier cosine series for the function f(x) = T – x, 0 < x < T. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1. Find the Fourier cosine series for the function f(x)= ™ – x, 0 < x < T. Problem 2. Find the integral o sin 3a cos 3a da. Problem 3. Expand the function f(x)= x, 0<x < 2, in half range sine series. (Hint: Take the odd extension of f(x). Then 21 = 4, l = 2.) Problem 4. Find a Fourier series for the function f(x)= x², 0 <x < 2. (Hint: Integrate the series in the Problem 3) Problem 5. Use Problem 4 to evaluate the series x (-1)"-'| n=1
Transcribed Image Text:Problem 1. Find the Fourier cosine series for the function f(x)= ™ – x, 0 < x < T. Problem 2. Find the integral o sin 3a cos 3a da. Problem 3. Expand the function f(x)= x, 0<x < 2, in half range sine series. (Hint: Take the odd extension of f(x). Then 21 = 4, l = 2.) Problem 4. Find a Fourier series for the function f(x)= x², 0 <x < 2. (Hint: Integrate the series in the Problem 3) Problem 5. Use Problem 4 to evaluate the series x (-1)"-'| n=1
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