A half-range periodic function f(x) is defined by { 0 < x < T, TT < x < 2n. T - x, f(x) 0, i. Sketch the graph of even extensions of f(x) in the interval ---4T < x < 6T and find its Fourier series. ii. Sketch the graph of odd extensions of f (x) in the interval -47 < x < 6A and find its Fourier series.

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A half-range periodic function f(x) is defined by
{
T - x,
0 < x < T,
f (x)
%3D
0,
TT < x < 2n.
i. Sketch the graph of even extensions of f(x) in the interval
--47T < x < 67 and find its Fourier series.
ii. Sketch the graph of odd extensions of f (x) in the interval
-47 < x < 6n and find its Fourier series.
Transcribed Image Text:A half-range periodic function f(x) is defined by { T - x, 0 < x < T, f (x) %3D 0, TT < x < 2n. i. Sketch the graph of even extensions of f(x) in the interval --47T < x < 67 and find its Fourier series. ii. Sketch the graph of odd extensions of f (x) in the interval -47 < x < 6n and find its Fourier series.
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