How do you use the Squeeze Theorem to find $lim (arctan(x) )/ (x)$ as x approaches infinity?

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Answer 1 · 2015-10-22T18:05:25

The limit is zero (see the reason using the Squeeze Theorem below).

Since $0 < arctan(x) < pi/2$ for all $x>0$ , we can say that $0 < arctan(x)/x < (pi/2)/x$ for all $x>0$ .

But $lim_{x->infty}0=0$ and $lim_{x -> infty} (pi/2)/x = 0$ .

Hence, by the Squeeze Theorem, $lim_{x->infty} arctan(x)/x = 0$ .

How do you use the Squeeze Theorem to find lim (arctan(x) )/ (x)lim (arctan(x) )/ (x) as x approaches infinity?