$\mathop {\lim }\limits_{x \to 0} {x^4}\cos \frac{1}{x} = ?$ Friday, March 18, 2022 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(cosine function is a bounded function lying between -1 to 1)= 0