# How do you find the limit of (sin2x)/x as x approaches infinity?

Oct 1, 2016

$= 0$

#### Explanation:

$\sin 2 x$ is a continuous periodic function bounded as $\sin 2 x \in \left[- 1 , 1\right]$

therefore

${\lim}_{x \to \infty} \frac{\sin 2 x}{x}$

$= {\lim}_{x \to \infty} \frac{c}{x}$ with $c \in \left[- 1 , 1\right]$

$= 0$