# Math Help - limit

1. ## limit

I need to show that lim[cos(x^2)/x] as x goes to infinity is zero and the limit of its derivative does not exist.

Thx

2. Originally Posted by math.link
I need to show that lim[cos(x^2)/x] as x goes to infinity is zero and the limit of its derivative does not exist.

Thx
$-1 \leq \cos x^2 \leq 1$...

3. Originally Posted by math.link
I need to show that lim[cos(x^2)/x] as x goes to infinity is zero and the limit of its derivative does not exist.

Thx
Looks pretty straight forward: since cos(t) always lies between -1 and 1,
[tex]-1/x\le cos(x^2)/x\le 1/x[/itex]. As x goes to infinity, both -1/x and 1/x go to 0.

As for proving that "the limit of its derivative does not exist", what is the derivative of $$cos(x^2)/x$$?