Question 1 Let f(r) be the 27-periodic function defined by x € [0, 7) -x- 2 rE (-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 = T/2

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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
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
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