Question

\[\lim_{x \rightarrow \frac{ \Pi }{ 2 }} (cosx)^{cosx}\]

Answer 1

use log.
take log on both sides.

Answer 2

ln y=cosx ln(cosx)

Answer 3

cos x * log cos x


(cosx / cos x) * -sinx + log cos x * - sinx

Answer 4

what is this ??
(cosx / cos x) * -sinx + log cos x * - sinx

Answer 5

you can use LH only if you have 0/0 or infinity/infinity form

Answer 6

Huh..i Just Forgot that..)

Answer 7

this is same as x^x x->0
try this
x^x = e^(x log(x))

Answer 8

so, log cos x/ sec x
now try LH

Answer 9

because cos =1/sec
that should work, i think....

Answer 10

that certainly works ... but this seems interesting ... using substitution.
let cos(x) = u, then we have u -> 0 , u^u ... i think you might have done before.

Answer 11

something like
-sin /(sec cos tan) = -cos
log L = 0
L=1

Answer 12

you got 2 methods :)
understood both ??

Answer 13

Yup..)