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Math Help - Lim x^3= a^3 when x ->a by epsilon-delta definition?

  1. #1
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    Lim x^3= a^3 when x ->a by epsilon-delta definition?

    so i got this 0<|x-a|<delta and |x^3-a^3|<epsilon and that is equal to |x-a||x^2+ax+a^2|<epsilon so i have to find a value that |x^2+ax+a^2|<value and |x^2+ax+a^2|=|x^2-2xa+a^2+3xa|<=|(x-a)^2|+|3xa| and i dont know what to do after this
    Last edited by yayovio; December 10th 2012 at 08:31 PM.
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  2. #2
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    Re: Lim x^3= a^3 when x ->a by epsilon-delta definition?

    You need to specify that \delta is less than some fixed value, say 1. Then |x^2+ax+a^2|<|(a+1)^2+a(a+1)+a^2|, and I'll call the right-hand side M. So if you specify \delta=\min(1,\frac{\epsilon}{M}), you should be able to write out the proof with that.

    There's a really good explanation of epsilon-delta proofs here at Math Help Forum - it's one of the four "sticky" threads at the top of the Calculus forum main page.

    - Hollywood
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