Hello everyone,

I am to use the delta-epsilon definition of a limit to show that the following limit does not exist. Unfortuantely, neither my instructor nor my textbook offer any worked examples or guides as to do this so I have been quite disillusioned so far. I have posted two attempts at proof below.

Thank you very much for your help.

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Prove that $\displaystyle \lim_{x \rightarrow 0} \frac{1}{x^2} $ does not exist.

__Proof #1:__ I came up with this but I don't think that it works because x depends solely on L. I think that delta should be in my $\displaystyle x $ somewhere since I have to show that for any $\displaystyle \delta > 0 $, the definition of a limit does not hold.

If I am indeed right about this problem, how should I modify my proof?

__Proof #2:__ I was suggested to use this value of x by my instructor. However, I don't understand how this version would generate a contradiction.