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Math Help - Proving a limit does not exist via delta epsilon

  1. #1
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    Proving a limit does not exist via delta epsilon

    The limit of 1/(x^2-4) does not exist as x approaches 2- this makes sense since for any delta there are value of x that are arbitrarily 'close' to 2, thus making 1/(x^2-4) infinitely large, so no possible L will make 1/(x^2-4)-L<epsilon for a given epsilon. However, I don't know how to turn this into a formal statement. Any tips?
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  2. #2
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    Quote Originally Posted by blarkark View Post
    The limit of 1/(x^2-4) does not exist as x approaches 2- this makes sense since for any delta there are value of x that are arbitrarily 'close' to 2, thus making 1/(x^2-4) infinitely large, so no possible L will make 1/(x^2-4)-L<epsilon for a given epsilon. However, I don't know how to turn this into a formal statement. Any tips?
    http://www.mathhelpforum.com/math-he...ta-proofs.html
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  3. #3
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    I would be interested to see a worked proof for this example. I've never seen an example of how to prove that a limit doesn't exist using epsilon-delta.
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