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Math Help - uniform continuity proof

  1. #1
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    uniform continuity proof

    Suppose that f:R-->R is continuous and has the property that for every epsilon>0, there is M>0 such that if abs(x)>=M, then abs(f(x))<epsilon. Show that f is uniformly continuos.
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  2. #2
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    Is this true? take f(x)= \frac{1}{x}
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  3. #3
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    The given function by Jose27 is not continuous.
    There are a lot of threads of similar questions. Observe that in [-M,M] a continuos function is always uniformly continuous and apply the condition for \varepsilon/2.
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