Periodic Functions : Bounded and Continuous
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1. A function f:R-->R is said to be periodic if there is a number p > 0 such that f(x) = f(x+p) for all xER . Show that a continuous periodic function on R is bounded and uniformly continuous.
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Periodic functions are shown to be bounded and continuous. The solution is detailed and well presented.
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Proof:
First, we consider the closed interval . Since is a continuous function, then is ...
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