Let f(r) be a function of period 27 such that * - 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(x) be a function of period 27 such that
16)= {
* - x, 0<r < *
0.
f(x) =
a) Sketch a graph of f(r) in the interval -27 <r < 27
b) Show that the Fourier series for f (x) in the interval 0 <r< 2n is
1
sr+
cos 3.r +
cos 5.r +.
32
52
1
1
+ sin r+ sin 2.r + sin 3r +; sin 4.r +...
1
c) By giving an appropriate value to r, show that
1
1+
32
1
8
52
Transcribed Image Text:Let f(x) be a function of period 27 such that 16)= { * - x, 0<r < * 0. f(x) = a) Sketch a graph of f(r) in the interval -27 <r < 27 b) Show that the Fourier series for f (x) in the interval 0 <r< 2n is 1 sr+ cos 3.r + cos 5.r +. 32 52 1 1 + sin r+ sin 2.r + sin 3r +; sin 4.r +... 1 c) By giving an appropriate value to r, show that 1 1+ 32 1 8 52
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