Problem: Is function unifomly continuous?












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Is sin ( 1/x ) uniformly continuous on set (1, + infinity) ?
I tried to prove that it is Lipschitz continuous but I got stuck.










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    Is sin ( 1/x ) uniformly continuous on set (1, + infinity) ?
    I tried to prove that it is Lipschitz continuous but I got stuck.










    share|cite|improve this question

























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      Is sin ( 1/x ) uniformly continuous on set (1, + infinity) ?
      I tried to prove that it is Lipschitz continuous but I got stuck.










      share|cite|improve this question













      Is sin ( 1/x ) uniformly continuous on set (1, + infinity) ?
      I tried to prove that it is Lipschitz continuous but I got stuck.







      uniform-continuity






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      asked Nov 18 at 15:42









      user560461

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          Certainly: it's differentiable with bounded first derivative. First property of Lipschitz continuous functions as listed on Wikipedia:




          An everywhere differentiable function $g : mathbb{R} to mathbb{R}$ is Lipschitz continuous (with $K = sup |g'(x)|$) if and only if it has bounded first derivative; one direction follows from the mean value theorem."







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            Certainly: it's differentiable with bounded first derivative. First property of Lipschitz continuous functions as listed on Wikipedia:




            An everywhere differentiable function $g : mathbb{R} to mathbb{R}$ is Lipschitz continuous (with $K = sup |g'(x)|$) if and only if it has bounded first derivative; one direction follows from the mean value theorem."







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              Certainly: it's differentiable with bounded first derivative. First property of Lipschitz continuous functions as listed on Wikipedia:




              An everywhere differentiable function $g : mathbb{R} to mathbb{R}$ is Lipschitz continuous (with $K = sup |g'(x)|$) if and only if it has bounded first derivative; one direction follows from the mean value theorem."







              share|cite|improve this answer
























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                Certainly: it's differentiable with bounded first derivative. First property of Lipschitz continuous functions as listed on Wikipedia:




                An everywhere differentiable function $g : mathbb{R} to mathbb{R}$ is Lipschitz continuous (with $K = sup |g'(x)|$) if and only if it has bounded first derivative; one direction follows from the mean value theorem."







                share|cite|improve this answer












                Certainly: it's differentiable with bounded first derivative. First property of Lipschitz continuous functions as listed on Wikipedia:




                An everywhere differentiable function $g : mathbb{R} to mathbb{R}$ is Lipschitz continuous (with $K = sup |g'(x)|$) if and only if it has bounded first derivative; one direction follows from the mean value theorem."








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                answered Nov 18 at 15:48









                Patrick Stevens

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