# Period Of Multiple Function

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**Period of Multiple Function:**

If f and g are periodic of period p then so is f g

**Proof :** Denote f g by h want h (x p) = h (x)

h (x p) = f (x p g(x p))

f (x) = g (x)

h (x) Where h is periodic of periods p.

If f is a periods of p then the graph of f repeats itself every p units.

Therefore if we know the curve of periodic function on Then we can draw the entire graph.

**Example:
**

If f is a periodic of period p then;

**Fourier Series:
**

Our purpose is to approximate periodic functions by sine and cosine. We define further Fourier Series of the periodic function f (x) by:

**Fourier Coefficients** a_{0}, a_{n} and b_{n} can be obtained by **Euler Formulas.**