limit of $6xsin(frac{4}{x})$ as $x$ approaches infinity

Limit of $6x\sin(\frac{4}{x})$ as $x$ approaches infinity. I know its $24$ thanks to wolfram alpha. I don't know how to get there. Just need to understand how this is done so I am not lost in the future.

Answer

Make a change of variable: ($n = 1/x$)

$$\lim_{x\to \infty}6x\sin \frac 4x=\lim_{n\to 0}\frac{6\sin 4n}{n}$$
$$=\lim_{n\to 0}\frac{24\sin 4n}{4n}$$
$$=\lim_{n\to 0}24\left(\frac{\sin 4n}{4n}\right)$$

$$=24$$