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Math Help - Proving a function is continuous

  1. #1
    xyz
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    Proving a function is continuous

    it is continuous because f(0) = 0. However, I'm not clear how to find such delta. We have to find a positive delta such that |f(x) - f(0)| < epsilon = |x sin(x) | < epsilon when |x sin x| < delta.

    How to find such delta? Does delta = epsilon? I'm not clear
    Last edited by xyz; November 18th 2009 at 10:02 PM.
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    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by xyz View Post


    Ofcourse it is continuous because f(0) = 0. However, I'm not clear how to find such delta. We have to find a positive delta such that |f(x) - f(0)| < epsilon = |x sin(x) | < epsilon when |x sin x| < delta.

    How to find such delta? Does delta = epsilon? I'm not clear
    Prove: |x|<\delta \implies |x\sin x|<\epsilon.

    Hint: |\sin x|\leq1
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