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Yahoo!

  • 3 years ago

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

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  1. hartnn
    • 3 years ago
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    use log. take log on both sides.

  2. ASAAD123
    • 3 years ago
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    ln y=cosx ln(cosx)

  3. Yahoo!
    • 3 years ago
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    cos x * log cos x (cosx / cos x) * -sinx + log cos x * - sinx

  4. hartnn
    • 3 years ago
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    what is this ?? (cosx / cos x) * -sinx + log cos x * - sinx

  5. hartnn
    • 3 years ago
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    you can use LH only if you have 0/0 or infinity/infinity form

  6. Yahoo!
    • 3 years ago
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    Huh..i Just Forgot that..)

  7. experimentX
    • 3 years ago
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    this is same as x^x x->0 try this x^x = e^(x log(x))

  8. hartnn
    • 3 years ago
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    so, log cos x/ sec x now try LH

  9. hartnn
    • 3 years ago
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    because cos =1/sec that should work, i think....

  10. experimentX
    • 3 years ago
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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.

  11. hartnn
    • 3 years ago
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    something like -sin /(sec cos tan) = -cos log L = 0 L=1

  12. hartnn
    • 3 years ago
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    you got 2 methods :) understood both ??

  13. Yahoo!
    • 3 years ago
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    Yup..)

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