Let f(r) be a function of period 2z such that f(x) = { S T - x, 0

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