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

Oct 22, 2015

Since $0 < \arctan \left(x\right) < \frac{\pi}{2}$ for all $x > 0$, we can say that $0 < \arctan \frac{x}{x} < \frac{\frac{\pi}{2}}{x}$ for all $x > 0$.
But ${\lim}_{x \to \infty} 0 = 0$ and ${\lim}_{x \to \infty} \frac{\frac{\pi}{2}}{x} = 0$.
Hence, by the Squeeze Theorem, ${\lim}_{x \to \infty} \arctan \frac{x}{x} = 0$.