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Math Help - y=x^3 (continuity)

  1. #1
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    y=x^3 (continuity)

    use the definition of epsilon-delta to proof f(x)=x^3 is continuous
    pls help to solve this
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  2. #2
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    Quote Originally Posted by chelloveck View Post
    use the definition of epsilon-delta to proof f(x)=x^3 is continuous
    pls help to solve this
    To show that f(x)= x^3 is continuous at x= a, you must show that
    "Given any \epsilon> 0, there exist \delta> 0 such that if |x- a|< \delta then |x^3- a^3|< \epsilon."

    It will help to recognize that |x^3- a^3|= |x- a||x^2+ ax+ a^2| so you will need to find an upper bound on |x^2+ ax+ a^2|.
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  3. #3
    Senior Member Pinkk's Avatar
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    If you're still stuck, observe that if |x-a| < 1, then |x| < 1 + |a| and then follow from that.
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