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Using Lipschitz continuity on open intervals

  1. Nov 11, 2013 #1
    1. The problem statement, all variables and given/known data

    Prove whether f(x) = x^3 is uniformly continuous on [-1,2)

    2. Relevant equations



    3. The attempt at a solution
    I used Lipschitz continuity. f has a bounded derivative on that interval, thus it implies f is uniformly continuous on that interval.

    But as it is not a closed interval, I am not sure I can use that approach. Any insight would be appreciated. Thanks.
     
  2. jcsd
  3. Nov 11, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Maybe you should look at the definition of uniform continuity. I'm not sure why you are concerned about whether the interval is closed or not.
     
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