I am having trouble figuring how to rigorously prove limits as $x \to \infty$. For instance, how would I rigorously prove that
$\lim_{x \to \infty} x^2 = \infty$
I am stumped. It is, of course, obvious. However, I do not think simply stating such a fact qualifies are a proper proof. Please note that a link to a resource that explains this would suffice as help.