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Question 1 Let f(x) be the 27-periodic function defined by r € [0, 7) -a- 2 rE [-T,0). f(x) = Then, the Fourier series of f (A) converges to -1/2 in r = 0 (B) converges to 1 in r = 0 (C) does not converge pointwise in all points where f is discontinuous (D) does not converge in x = =/2

Question 1 Let f(x) be the 27-periodic function defined by r € [0, 7) -a- 2 rE [-T,0). f(x) = Then, the Fourier series of f (A) converges to -1/2 in r = 0 (B) converges to 1 in r = 0 (C) does not converge pointwise in all points where f is discontinuous (D) does not converge in x = =/2

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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I'm trying to solve this with the table given, but i can't seem to understand it please if possible can you solve it with a bit of an explanation on each step?
27 f(r) ~ ao + 27 k. T ak cos ( k-I+ be sin f(#) dr, 27 f(r) cos (k 2 | f) sin ( k ao ak = dr k 1, dr k 1. | SOf dz = Taổ + (af + bi) (identità di Parseval) k=1
Transcribed Image Text:27 f(r) ~ ao + 27 k. T ak cos ( k-I+ be sin f(#) dr, 27 f(r) cos (k 2 | f) sin ( k ao ak = dr k 1, dr k 1. | SOf dz = Taổ + (af + bi) (identità di Parseval) k=1
Question 1 Let f(x) be the 27-periodic function defined by a € [0, T) -T-2 a E [-7, 0). 1+1 f(x) = Then, the Fourier series of f (A) converges to -1/2 in r= 0 (B) converges to 1 in r = 0 (C) does not converge pointwise in all points where f is discontinuous (D) does not converge in r = =/2
Transcribed Image Text:Question 1 Let f(x) be the 27-periodic function defined by a € [0, T) -T-2 a E [-7, 0). 1+1 f(x) = Then, the Fourier series of f (A) converges to -1/2 in r= 0 (B) converges to 1 in r = 0 (C) does not converge pointwise in all points where f is discontinuous (D) does not converge in r = =/2
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