Let f(x) be a function of period 27 such that f(a) =5 over the interval 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercises 1
Let f(x) be a function of period 27 such that
f(r) = 5
over the interval 0 <r < 2n.
a) Sketch a graph of f(x) in the interval 0<r < 4n
b) Show that the Fourier series for f(x) in the interval 0<x< 2n is
1
1
sin 2r +
3
- sin r +
2
sin 3.r +.
c) By giving an appropriate value to r, show that
1
1
1
1-
3
1
%3D
-...
9
Exercises 2
Let f(r) be a function of period 27 such that
{
T - r, 0<a < T
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(a) in the interval 0<r< 27 is
2
COs r+
1
cos 3.r +
32
1
cos 5r +...
52
4.
1
sin a+
sin 3.r+
1
sin 4.r +...
sin 2.r +
3
c) By giving an appropriate value to r, show that
= 1+
32
+...
52
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