anonymous
  • anonymous
\[\lim_{x \rightarrow \frac{ \Pi }{ 2 }} (cosx)^{cosx}\]
Mathematics
schrodinger
  • schrodinger
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hartnn
  • hartnn
use log. take log on both sides.
anonymous
  • anonymous
ln y=cosx ln(cosx)
anonymous
  • anonymous
cos x * log cos x (cosx / cos x) * -sinx + log cos x * - sinx

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hartnn
  • hartnn
what is this ?? (cosx / cos x) * -sinx + log cos x * - sinx
hartnn
  • hartnn
you can use LH only if you have 0/0 or infinity/infinity form
anonymous
  • anonymous
Huh..i Just Forgot that..)
experimentX
  • experimentX
this is same as x^x x->0 try this x^x = e^(x log(x))
hartnn
  • hartnn
so, log cos x/ sec x now try LH
hartnn
  • hartnn
because cos =1/sec that should work, i think....
experimentX
  • experimentX
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.
hartnn
  • hartnn
something like -sin /(sec cos tan) = -cos log L = 0 L=1
hartnn
  • hartnn
you got 2 methods :) understood both ??
anonymous
  • anonymous
Yup..)

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