calculus - What is the limit of $limlimits_{x→∞}frac{sin x}{x}$

How do I evaluate this limit: $$\lim\limits_{x\to \infty}\frac{\sin x}{x}$$

Is it $0$? If yes, how so?

Answer

we can see that for $x>0$ we have
$$-\frac{1}{x}\le\frac{\sin x}{x}\le+\frac{1}{x}$$
then by squeeze theorem you can conclude that $\lim\limits_{x\to+\infty}\frac{\sin x}{x}=0$ since $\lim\limits_{x\to+\infty}-\frac{1}{x}=\lim\limits_{x\to+\infty}+\frac{1}{x}=0$