Question

A function f: R R is considered periodic on R if there exists a number p > 0 such that f(x+P) = f(x) for all x R. Prove that a continuous periodic function on R is bounded and uniformly continuous on R.

Name: a function f r r is considered periodic on r if there exists a number p 0 such that fxp fx for all x r prove that a continuous periodic function on r is bounded and uniformly continuous on r 52723
Uploaded: 2022-11-03T18:44:40-08:00
Duration: 1 min 26 s
Channel: Carson Merrill
Description: a function f r r is considered periodic on r if there exists a number p 0 such that fxp fx for all x r prove that a continuous periodic function on r is bounded and uniformly continuous on r 52723

          A function f: R  R is
considered periodic on R if there exists a number p > 0 such
that f(x+P) = f(x) for all x  R.
Prove that a continuous periodic function on R is bounded and
uniformly continuous on R.

Added by Ismael F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

11/03/2022

Step 1

First, we need to find a number p such that f(x+p) = f(x) for all x in R. Show more…

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A function f: R R is considered periodic on R if there exists a number p > 0 such that f(x+P) = f(x) for all x R. Prove that a continuous periodic function on R is bounded and uniformly continuous on R.