# Math Help - Limit

1. ## Limit

Determine the value of:

2. Originally Posted by Apprentice123
Determine the value of:

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

CB

3. 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

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