A half range periodic function f(x) is defined by f(r) = x – 1, 0 < x < 1, f(r) = f(x +2). i. Sketch the graph of even extensions of f(x) in the interval –4 < x < 4 and find its Fourier series. ii. Sketch the graph of odd extensions of f(r) in the interval –4

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Chapter2: Second-order Linear Odes
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A half range periodic function f(x) is defined by
f (x) = x – 1, 0 < x < 1,
f (x) = f(x +2).
i. Sketch the graph of even extensions of f(x) in the interval –4 < x < 4
and find its Fourier series.
ii. Sketch the graph of odd extensions of f(x) in the interval -4 < x < 4
and find its Fourier series.
Transcribed Image Text:A half range periodic function f(x) is defined by f (x) = x – 1, 0 < x < 1, f (x) = f(x +2). i. Sketch the graph of even extensions of f(x) in the interval –4 < x < 4 and find its Fourier series. ii. Sketch the graph of odd extensions of f(x) in the interval -4 < x < 4 and find its Fourier series.
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