2. Assume that f(x) is periodic with period 27 and, for <<, is given by the formula f(x) N 0 if 24 f(x)=x² if 0

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Assume that f(x) is periodic with period 27 and, for <<, is given by the
formula
f(x) N
0 if
24
f(x)=x² if
0
<x<
(a) Sketch the graph of f for a between -37 and 3m.
(b) Prove that the Fourier series of f(a) is given by
if
-*<2<-
(2 cos(nr/2)
n²
(²n² − 8) sin(n/2)) cos(x).
+
2³
(c) Determine the value to which this series converges when z = T/2. Explain your
reasoning.
Transcribed Image Text:2. Assume that f(x) is periodic with period 27 and, for <<, is given by the formula f(x) N 0 if 24 f(x)=x² if 0 <x< (a) Sketch the graph of f for a between -37 and 3m. (b) Prove that the Fourier series of f(a) is given by if -*<2<- (2 cos(nr/2) n² (²n² − 8) sin(n/2)) cos(x). + 2³ (c) Determine the value to which this series converges when z = T/2. Explain your reasoning.
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