# Math Help - prove that (arctan x)<x if x is positive

1. ## prove that (arctan x)<x if x is positive

It seems like this should be a fairly simple thing, yet I can't seem to pin down the trick.

Hi, all. I need to prove that if $x>0$, then $\tan^{-1}x.

Any ideas?

POTENTIALLY USELESS INFO: This is in order to prove that $\{x_n\}$ recursively defined by $x_{n+1}=\tan^{-1}x_n$ $\forall$ $n\geq 0$ and $x_0>0$ converges to a finite limit.

Thanks!

2. x - arctan(x) is continuous and is 0 at 0, its derivative is 1 - 1/(1+x^2) which is positive when x>0 .... I see no problem here, it is an increasing function.