# Thread: Another limit problem

1. ## Another limit problem

Can you help with the problem below ?

$
\lim_{x\to{{\pi}\over{2}}^-}\left(\tan x\right)^{\cos x}
$

2. Originally Posted by azarue
Can you help with the problem below ?

$
\lim_{x\to{{\pi}\over{2}}^-}\left(\tan x\right)^{\cos x}
$

$\lim_{x\to{{\pi}\over{2}}^-}\left(\tan x\right)^{\cos x}$
$= exp \{\ \lim_{x\to{{\pi}\over{2}}^-} \cos(x) \ln(\tan(x)) \}\$
$= exp \{\ \lim_{x\to{{\pi}\over{2}}^-} \sin(x) \frac{\ln(\tan(x))}{\tan(x)} \}\$
We know $\lim_{u\to\infty} \frac{ \ln(u) }{u} = 0$
$exp \{\ 0 \}\ = 1$