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Math Help - Another limit problem

  1. #1
    Junior Member
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    Another limit problem

    Can you help with the problem below ?

    <br />
\lim_{x\to{{\pi}\over{2}}^-}\left(\tan x\right)^{\cos x}<br />

    Thanks in advance.
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  2. #2
    Super Member
    Joined
    Jan 2009
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    Quote Originally Posted by azarue View Post
    Can you help with the problem below ?

    <br />
\lim_{x\to{{\pi}\over{2}}^-}\left(\tan x\right)^{\cos x}<br />

    Thanks in advance.

     \lim_{x\to{{\pi}\over{2}}^-}\left(\tan x\right)^{\cos x}

     = exp \{\ \lim_{x\to{{\pi}\over{2}}^-} \cos(x) \ln(\tan(x)) \}\

      = exp \{\ \lim_{x\to{{\pi}\over{2}}^-} \sin(x) \frac{\ln(\tan(x))}{\tan(x)} \}\

    We know  \lim_{u\to\infty} \frac{ \ln(u) }{u} = 0

    so it is equal to
     exp \{\ 0 \}\ = 1
    Last edited by simplependulum; May 24th 2010 at 05:24 PM.
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