A real-valued function f is said to be periodic with period T if f(x T ) f(x). For
Chapter 11, Problem 21(choose chapter or problem)
A real-valued function f is said to be periodic with period T if f(x T ) f(x). For example, 4p is a period of sin x, since sin(x 4p) sin x. The smallest value of T for which f(x T ) f(x) holds is called the fundamental period of f. For example, the fundamental period of f(x) sin x is T 2p. What is the fundamental period of each of the following functions? (a) f(x) cos 2px (b) (c) f(x) sin x sin 2x (d) f(x) sin 2x cos 4x (e) f(x) sin 3x cos 2x (f) An and Bn depend only on n f(x) A0 n1 An cos n p x Bn sin n p x, f(x) si
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