# Thread: Limit when x go´s to 0

1. ## Limit when x go´s to 0

Hi!
Can you help me with this problem?

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

2. 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.

3. Ok,Thank you. Anyone els?

4. 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