# 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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## marked as duplicate by Arturo Magidin, Ryan Budney, Gerry Myerson, Sasha, Alex BeckerFeb 19 '12 at 6:45

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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

## 1 Answer

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Especially Robert Israel’s answer, which makes the right intuition crystal clear. –  Brian M. Scott Feb 19 '12 at 4:13
That's called a classic trick question-it tricks you into overthinking the problem. This is why recognizing patterns is so important in practical problem solving! –  Mathemagician1234 Feb 19 '12 at 7:06