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 03:58
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@ChangweiZhou : Who is Arnold? – jimjim Feb 19 '12 at 04:02
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@V.I.Arnold. Also apologize for confusing the sign. – Kerry Feb 19 '12 at 04:07
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I knew I'd seen this before here: duplicate. – Arturo Magidin Feb 19 '12 at 05:16
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Especially Robert Israel’s answer, which makes the right intuition crystal clear. – Brian M. Scott Feb 19 '12 at 04:13
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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 07:06