Originally Posted by

**joatmon** I'm trying to understand the proof of this function:

$\displaystyle

\displaystyle \lim_{x\to 0 } x^2cos 20 \pi x =0}

$

Here is the part that I understand:

Let $\displaystyle f(x)=-x^2, g(x)=x^2cos 20 \pi x, h(x)=x^2$

Then, $\displaystyle -1 \leq cos 20 \pi x \leq 1$

But then, they go on to state this, which I can't figure out:

$\displaystyle -x^2 \leq x^2cos 20 \pi x \leq x^2$

What I don't understand is how the x-squared terms can always be either less than -1 or greater than 1. I understand that the middle term oscillates between -1 and 1, but how do we know what x-squared is?

Can anybody help me understand this?

Thanks.