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\[\lim_{x \rightarrow \frac{ \Pi }{ 2 }} (cosx)^{cosx}\]
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hartnn
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use log.
take log on both sides.
ASAAD123
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ln y=cosx ln(cosx)
Yahoo!
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cos x * log cos x
(cosx / cos x) * -sinx + log cos x * - sinx
hartnn
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what is this ??
(cosx / cos x) * -sinx + log cos x * - sinx
hartnn
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you can use LH only if you have 0/0 or infinity/infinity form
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Huh..i Just Forgot that..)
experimentX
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this is same as x^x x->0
try this
x^x = e^(x log(x))
hartnn
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so, log cos x/ sec x
now try LH
hartnn
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because cos =1/sec
that should work, i think....
experimentX
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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
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something like
-sin /(sec cos tan) = -cos
log L = 0
L=1
hartnn
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you got 2 methods :)
understood both ??
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Yup..)