# How do you use the Squeeze Theorem to find lim (x^2)(cos20(pi*x))  as x approaches zero?

Refer to explanation

#### Explanation:

W know that

$- 1 \le \cos \left(20 \pi x\right) \le 1 \implies - {x}^{2} \le {x}^{2} \cos \left(20 \pi x\right) \le {x}^{2}$

Hence using the squeeze theorem since

${\lim}_{x \to 0} - {x}^{2} = {\lim}_{x \to 0} {x}^{2} = 0$

then

${\lim}_{x \to 0} {x}^{2} \cos \left(20 \pi x\right) = 0$