# Math Help - Limit Tan and cos

1. ## Limit Tan and cos

Calculate :
$
\lim_{x\to +\infty }(x^{2}+xtan(x))
$

$\lim_{x\to +\infty }(\sqrt{\cos (2\Pi x)-1})$

2. Originally Posted by dhiab
Calculate :
$
\lim_{x\to +\infty }(x^{2}+xtan(x))
$

$\lim_{x\to +\infty }(\sqrt{\cos (2\Pi x)-1})$
It's pretty obvious, isn't it, that the first will go to infinity (there is no limit).

And the second also does not have a limit because it oscillates.

3. Originally Posted by HallsofIvy
It's pretty obvious, isn't it, that the first will go to infinity (there is no limit).

And the second also does not have a limit because it oscillates.
I disagree. The first one oscillates between positive and negative infinity, and hence has no limit.
The second one is undefined for all but integer values of x, in which case it evaluates to 0. So it's limit is undefined.