Q:

calculate the limit $\lim\limits_{x \to0} \frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}$

Possible Duplicate:
Crafty solutions to the following limit 

A problem in a trivium was:
$$\lim\limits_{x \to 0} \frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}$$

A:

Check this article:
https://mathoverflow.net/questions/20696/a-question-regarding-a-claim-of-v-i-arnold

