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Thread: Uniform continuity

  1. November 13th 2010, 03:39 AM #1
    james_bond
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    Uniform continuity

    Show that f(x)=\frac 1{x-1} is not uniformly continuous on (1,6).
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  2. November 13th 2010, 07:41 AM #2
    FernandoRevilla
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    Take \epsilon=10.

    Suppose there exists 0<\delta<1 satisfyng the definition of uniform convergence.

    Choose x=1+\delta,\;y=1+\delta/11.

    Prove that |x-y|<\delta and |f(x)-f(y)|>10 (absurd)

    Regards.
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