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

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Rogue
 3 years ago
Best ResponseYou've already chosen the best response.1This seems like an interesting little problem...\[y = \lim_{x \rightarrow \frac {\pi}{2}} (\sin x)^{\tan x}\]\[\ln y = \ln \lim_{x \rightarrow \frac {\pi}{2}} (\sin x)^{\tan x} \rightarrow \ln y = \lim_{x \rightarrow \frac {\pi}{2}} \tan x \ln (\sin x)\]\[\ln y = \lim_{x \rightarrow \frac {\pi}{2}} \tan x \ln (\sin x) \rightarrow \ln y = \lim_{x \rightarrow \frac {\pi}{2}} \frac {\sin x \ln (\sin x)}{\cos x} = \frac {0}{0}\]

Rogue
 3 years ago
Best ResponseYou've already chosen the best response.1Now you'll have to use L'Hopital's rule to evaluate that. Can you do that or need me to run you through it?

suju101
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \infty} (lnx)^{1/x}\] can you please help me with this probelm too..
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