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Math Help - Limit

  1. #1
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    Limit

    Determine the value of:


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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Apprentice123 View Post
    Determine the value of:





    What do you mean by cotgx? Use brackets and explain any remaining notation please.

    CB
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  3. #3
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    Hello, Apprentice123!

    Determine the value of: . \lim_{x\to\pi^+} \log_{\frac{1}{2}}\cot x

    We have: . \log_{\frac{1}{2}}\cot x \;=\;\frac{\ln(\cot x)} {\ln\left(\frac{1}{2}\right)} \;=\;\frac{\ln(\tan x)^{-1}} {\ln(2)^{-1}} . = \;\frac{-\ln(\tan x)}{-\ln(2)} \;=\;\frac{\ln(\tan x)}{\ln(2)}

    Then: . \lim_{x\to\pi^+}\frac{\ln(\tan x)}{\ln(2)} \;=\;\frac{\ln(\tan\pi)}{\ln(2)} \;=\;\frac{\ln(0)}{\ln(2)} \;=\;-\infty<br /> <br />

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