Answer
$$\lim _{x \rightarrow \infty}\sin \frac{1}{x}=0 .$$
Work Step by Step
When $ x\to \infty $ the function $\frac{1}{x}\to 0$ and hence $\sin \frac{1}{x}\to \sin 0=0$. But when $ x\to 0$ the function $\frac{1}{x}\to \infty $ and hence $\sin \frac{1}{x}\to \sin \infty $ and the function $\sin x $ oscillates indefinitely. Thus, we have
$$\lim _{x \rightarrow \infty}\sin \frac{1}{x}=0 .$$
