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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

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    f is continuous on R, and it looks like it has a bounded derivative on R\[-1,1].
     
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