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Math Help - Prove a limit using the delta epsilon method

  1. #1
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    Prove a limit using the delta epsilon method

    Hello,
    How can I prove that the limit of the following function equals to zero, using the delta epsilon method?
     \lim_{x\rightarrow 2}(x^2-4)=0

    I have reached this step, but I do not know what to do next:
    |x-2|< \frac{\varepsilon}{|x+2|}

    thanks in advance, Michael
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  2. #2
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    Quote Originally Posted by msokol89 View Post
    Hello,
    How can I prove that the limit of the following function equals to zero, using the delta epsilon method?
     \lim_{x\rightarrow 2}(x^2-4)=0
    I have reached this step, but I do not know what to do next:
    |x-2|< \frac{\varepsilon}{|x+2|}
    If you know that |x-2|<1 then we know that |x+2|<5.
    Pick \delta  = \min \left\{ {1,\frac{\varepsilon }{5}} \right\}.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Hint :

    In [1,3] we have |x+2|\leq 5 so, choose \delta=\min \{1,\epsilon/5\}



    Edited: Sorry, I didn't see Plato's post.
    Last edited by FernandoRevilla; March 4th 2011 at 10:13 AM.
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  4. #4
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    I understand, thanks to you both
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