Question

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

Answer 1

Refer to explanation

Explanation:

W know that

`-1<=cos(20pix)<=1=>-x^2<=x^2cos(20pix)<=x^2`

Hence using the squeeze theorem since

`lim_(x->0)-x^2=lim_(x->0)x^2=0`

then

`lim_(x->0) x^2cos(20pix)=0`