limits and infinity I'm having trouble wrapping my head around some of the 'rules' of limits. For example,
$$
\lim_{x\to \infty} \sqrt{x^2 -2} - \sqrt{x^2 + 1}
$$
becomes
$$
\sqrt{\lim_{x\to \infty} (x^2) -2} - \sqrt{\lim_{x\to \infty}(x^2) + 1}
$$
which, after graphing, seems to approach zero. My question is how do you know for sure the answer is zero without graphing? Thanks!

Hint: $$\left[\sqrt {x^2 - 2} - \sqrt{x^2 + 1}\right]\dot\, \frac{\sqrt {x^2 - 2} + \sqrt{x^2 + 1}}{\sqrt {x^2 - 2} + \sqrt{x^2 + 1}} = \frac{x^2 - 2 - (x^2 + 1)}{\sqrt {x^2 - 2} + \sqrt{x^2 + 1}}$$
