How to do limits approaching infinity with trig?

Question

$$\lim_{x\to\infty} \frac{\sin 2x}{x}$$

This is the math problem, but how do I do limits approaching to infinity with trig?

Answer 1

Hints:

$$0 \le \left|\frac{\sin 2x}{x}\right| \le \frac{1}{|x|}$$

Answer 2

HINT $-1 \leq \sin 2x\leq 1$ and $\lim_{x\to \infty} \frac{1}{x} = 0$

Answer 3

Hint: $0\le|\sin 2x|\le1\, \forall x$, however as $x\to \infty, \frac1x \to 0$