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Thread: uniformly continuous

  1. #1
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    uniformly continuous

    Hello... i was trying to do this but stuck in between ...can anyone help me?

    F (x)= xsin (1/x): x not equal to 0
    F (x)= 0 : for x=0
    For all x belongs closed interval -1,1..
    Prove f (x) is uniformly continuous by using defination?
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  2. #2
    MHF Contributor

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    Re: uniformly continuous

    A Euro definition? Do you have to buy it? I assume you mean the \delta-\epsilon definition: a function, f, is "uniformly continuous" on set A if and only if, for every \epsilon> 0 there exist \delta> 0 such that if for all x\in A if |x- a|<\delta then |f(x)- f(a)|< \epsilon.
    (The difference between "continuous" and "uniformly continuous" is the if a function is uniformly continuous on set A, we can choose a \delta that works for all a in A. If the function is only continuous, possible values for \delta may depend both \epsilon and a.)
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