Exercises 2 Let f(a) be a function of period 27 such that { T - a, 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(a) be a function of period 27 such that
0 < x <T
f(x) = {
T - x.
0.
T < a < 27
a) Sketch a graph of f(r) in the interval -2T < x < 27
b) Show that the Fourier series for f(x) in the interval 0< a < 27 is
cos z + cos 3r +
1
Cos a
1
cos 3x +
52
cos Sr +...
4
1
sin 3r +
3
1
sin 4.r +...
4
sin a +
sin 2x+
c) By giving an appropriate value to r, show that
1
=1+
32
1
+...
52
8.
Transcribed Image Text:Exercises 2 Let f(a) be a function of period 27 such that 0 < x <T f(x) = { T - x. 0. T < a < 27 a) Sketch a graph of f(r) in the interval -2T < x < 27 b) Show that the Fourier series for f(x) in the interval 0< a < 27 is cos z + cos 3r + 1 Cos a 1 cos 3x + 52 cos Sr +... 4 1 sin 3r + 3 1 sin 4.r +... 4 sin a + sin 2x+ c) By giving an appropriate value to r, show that 1 =1+ 32 1 +... 52 8.
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