Let f(a) be a function of period 27 such that { T - r, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Exercises 2
Let f(x) be a function of period 27 such that
T - r, 0<x < 7
T <a < 2n
f(x) =
0,
a) Sketch a graph of f(r) in the interval -27 <r < 27
b) Show that the Fourier series for f(r) in the interval 0 <r < 27 is
1
cos 3.r +
32
1
cos 5.r +.
52
COS +
4
1
+ sin a + sin 2r +sin 3r+
1
1
-sin 4r+...
c) By giving an appropriate value to r, show that
1
1
1+
32
8
52
Transcribed Image Text:Exercises 2 Let f(x) be a function of period 27 such that T - r, 0<x < 7 T <a < 2n f(x) = 0, a) Sketch a graph of f(r) in the interval -27 <r < 27 b) Show that the Fourier series for f(r) in the interval 0 <r < 27 is 1 cos 3.r + 32 1 cos 5.r +. 52 COS + 4 1 + sin a + sin 2r +sin 3r+ 1 1 -sin 4r+... c) By giving an appropriate value to r, show that 1 1 1+ 32 8 52
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