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

Possible Duplicate:
Crafty solutions to the following limit

A problem in a trivium was:

$$\lim\limits_{x \to 0} \frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}$$

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If I am not mistaken this is a problem from Arnold. A google search or something can give a quick answer on this. The result is -1. –  Kerry Feb 19 '12 at 3:58
@ChangweiZhou : Who is Arnold? –  Arjang Feb 19 '12 at 4:02
@V.I.Arnold. Also apologize for confusing the sign. –  Kerry Feb 19 '12 at 4:07
I knew I'd seen this before here: duplicate. –  Arturo Magidin Feb 19 '12 at 5:16