# Find the limit as x approaches infinity of y=sinx/x?

Mar 21, 2018

${\lim}_{x \to \infty} \sin \frac{x}{x} = 0$

#### Explanation:

You're going to want to use the squeeze theorem for this. Recall that $\sin x$ is only defined on -1 ≤ sinx ≤ 1. Therefore

-1/x ≤ sinx/x ≤ 1/x

And since ${\lim}_{x \to \infty} - \frac{1}{x} = {\lim}_{x \to \infty} \frac{1}{x} = 0$, then ${\lim}_{x \to \infty} \sin \frac{x}{x} = 0$.

Hopefully this helps!