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
$$\sqrt{x^2 -2} - \sqrt{x^2 + 1}=(\sqrt{x^2 -2} - \sqrt{x^2 + 1})\cdot \frac{\sqrt{x^2 -2} + \sqrt{x^2 + 1}}{\sqrt{x^2 -2} +\sqrt{x^2 + 1}}=\frac{-3}{\sqrt{x^2 -2} + \sqrt{x^2 + 1}}$$
