# Limit when x go´s to 0

• September 17th 2009, 08:49 AM
Kluringen
Limit when x go´s to 0
Hi!
Can you help me with this problem?

$\lim_{x\ ->\ 0}\frac{\sin 2x \cot\frac{x}{3} \ln(1+4x)}{\arctan 5x}$
• September 17th 2009, 11:17 AM
redsoxfan325
I can tell you (or rather Maple 12 can tell you) that the answer is $\frac{24}{5}$, but I have no idea how to analytically evaluate the limit. Sorry I can't be more help.
• September 17th 2009, 10:07 PM
Kluringen
Ok,Thank you. Anyone els?
• September 17th 2009, 10:10 PM
Jose27
Quote:

Originally Posted by Kluringen
Hi!
Can you help me with this problem?

$\lim_{x\ ->\ 0}\frac{\sin 2x \cot\frac{x}{3} \ln(1+4x)}{\arctan 5x}$

$\lim_{x\ \rightarrow 0}\frac{\sin 2x \cot\frac{x}{3} \ln(1+4x)}{\arctan 5x} = \lim_{x\ \rightarrow 0}\frac{\sin 2x \ln(1+4x)}{\arctan 5x \tan\frac{x}{3}}$ Now try using L'Hopital's rule