Exercises 2 Let f(æ) be a function of period 27 such that f(1) = {" *- a, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercises 2
Let f(x) be a function of period 27 such that
12) - {*
T - x, 0<r < T
f (x):
0,
T <r < 2n
a) Sketch a graph of f(r) in the interval -2n <I< 2n
b) Show that the Fourier series for f(r) in the interval 0 <r < 2r is
1
cos 3.x +
32
1
cos 5x +...
52
1
1
1
+ sin a + sin 2a + sin 3x+
4
sin 4r +...
2
3
c) By giving an appropriate value to r, show that
1
=1+
32
1
+...
52
Transcribed Image Text:Exercises 2 Let f(x) be a function of period 27 such that 12) - {* T - x, 0<r < T f (x): 0, T <r < 2n a) Sketch a graph of f(r) in the interval -2n <I< 2n b) Show that the Fourier series for f(r) in the interval 0 <r < 2r is 1 cos 3.x + 32 1 cos 5x +... 52 1 1 1 + sin a + sin 2a + sin 3x+ 4 sin 4r +... 2 3 c) By giving an appropriate value to r, show that 1 =1+ 32 1 +... 52
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