1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Real Analysis: Uniformly continuous

  1. Mar 11, 2006 #1
    Please help me with this one:

    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
  2. jcsd
  3. Mar 11, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    By teh (second?) Fundamental Theorem of Calculus, F, in part a), is a differentiable function with (uniformly) bounded derivative. It is a standard exercise to show this is uniformly continuous, so what do you think you need to do now you've got this (slightly) different way of thinking about it?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Real Analysis: Uniformly continuous