Math Help - Squeeze Theorem

1. Squeeze Theorem

Use the squeeze theorem to show that lim as n goes to infinity arctan(n^2)/Sqrt(n) = 0

Use the squeeze theorem to show that lim as n goes to infinity arctan(n^2)/Sqrt(n) = 0
note that $- \frac {\pi}2 \le \arctan x \le \frac {\pi}2$ for all $x$, thus we have

$- \frac {\pi}{2 \sqrt{n}} \le \frac {\arctan (n^2)}{\sqrt{n}} \le \frac {\pi}{2 \sqrt{n}}$

can you finish?

(also, note that we can make the left side zero, but this looks nice for symmetry )

3. Im just kinda confused on how you end up with zero from that : /

$\lim_{n \to \infty} - \frac {\pi}{2 \sqrt{n}} \le \lim_{n \to \infty} \frac {\arctan (n^2)}{\sqrt{n}} \le \lim_{n \to \infty} \frac {\pi}{2 \sqrt{n}}$