Is the limit of 1/x^2 as x approaches 0 non-existent?

[JG89]

Obviously $$\lim_{x \rightarrow 0} \frac{1}{x^2} = \infty$$, but am I correct in saying that the limit as x approaches 0 of $$\frac{1}{x^2}$$ doesn't exist?

If it did exist then one of the conditions would be, for values of x sufficiently close to 0, $$|x-\infty| = \infty < \delta$$ which obviously isn't true for all positive values of delta. Am this correct?

 

[snipez90]

I think you are correct in saying that the limit does not exist. However,

$$\lim_{x \rightarrow a} f(x) = \infty$$ means that for every $$N \in \Re$$ there exists a number $$\delta > 0$$ such that, for all x,
if $$0 < |x-a| < \delta$$, then $$f(x) > N$$.

 

[JG89]

I don't know how I made that mistake :rofl:

Thanks for the reply though :)