# What is the limit of  xsin(1/x) as x goes to infinity?

${\lim}_{x \rightarrow \infty} x \sin \left(\frac{1}{x}\right) = {\lim}_{x \rightarrow \infty} \sin \frac{\frac{1}{x}}{\frac{1}{x}} = 1$
Use ${\lim}_{\theta \rightarrow 0} \sin \frac{\theta}{\theta} = 1$ and
${\lim}_{x \rightarrow \infty} \frac{1}{x} = 0$