## 15.EXAMPLE -HALF RANGE FOURIER SINE SERIES EXAMPLE BY ENGINEERING CLASSES FOR PTU, GNDU BSNL, GATE EXAM

EXAMPLE OF FOURIER HALF RANGE SERIESÂ

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EVEN FUNCTION

A function y = f(x) is said to be even, if f(-x) = f(x). The graph of the even function is always symmetrical about the y-axis.

ODD FUNCTION

A function y=f(x) is said to be odd, if f(-x) = – f(x). The graph of the odd function is always symmetrical about the origin. For example, the function f(x) = in [-1,1] is even as f(-x) = = f(x) and the function f(x) = x in [-1,1] is odd as f(-x) = -x = -f(x). The graphs of these functions are shown below : 1. If f(x) is even and g(x) is odd, then