### $\mathop {\lim }\limits_{x \to 0} {x^4}\cos \frac{1}{x} = ?$
The given limit $= \mathop {\lim }\limits_{x \to 0} {x^4} \times \mathop {\lim }\limits_{x \to 0} \cos \frac{1}{x}$
$= 0 \times$ a finite number