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Suppose f is a continuous real valued function on R - real #s and that 0<f(x)<3 for every x in R. Let F(x) = integral from 0 to x of f(t) dt.

a) Show that F is uniformly continuous on R

b) Suppose the continuity assumption is left out, but the function f is still assumed to have 0<f(x)<3 for all x and to be integrable on every bounded interval. Must the conclusion of uniform continuity of F on R still be true? Prove or give counterexample.

Thank You for your help

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# Homework Help: Real Analysis: Uniformly continuous

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