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!

Homework Help: F(x) = x * sin(1/x) for x =/=0 and f(0) = 0. continuous on R?

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Is the function f(x) = x * sin(1/x) for x =/= 0 and f(0) = 0 unifoirmly continuous on R?


    2. Relevant equations



    3. The attempt at a solution

    dom(f) = (-inf, inf)



    x,y in R and |x-y| < d imply |f(x) - f(y)| < e

    |x - 0| < d imply |x * sin(1/x) - 0 | < e

    ?
     
  2. jcsd
  3. Nov 14, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    f is continuous on R, and it looks like it has a bounded derivative on R\[-1,1].
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook