## suju101 3 years ago lim (sin x )^tanx as x->pi/2

1. Rogue

This seems like an interesting little problem...$y = \lim_{x \rightarrow \frac {\pi}{2}} (\sin x)^{\tan x}$$\ln y = \ln \lim_{x \rightarrow \frac {\pi}{2}} (\sin x)^{\tan x} \rightarrow \ln y = \lim_{x \rightarrow \frac {\pi}{2}} \tan x \ln (\sin x)$$\ln y = \lim_{x \rightarrow \frac {\pi}{2}} \tan x \ln (\sin x) \rightarrow \ln y = \lim_{x \rightarrow \frac {\pi}{2}} \frac {\sin x \ln (\sin x)}{\cos x} = \frac {0}{0}$

2. Rogue

Now you'll have to use L'Hopital's rule to evaluate that. Can you do that or need me to run you through it?

3. suju101

i'll try

4. suju101

$\lim_{x \rightarrow \infty} (lnx)^{1/x}$ can you please help me with this probelm too..