Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Babyslapmafro

  • 3 years ago

Please help me find the limit of the following function (click to see).

  • This Question is Closed
  1. Babyslapmafro
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\lim_{x \rightarrow 0^+}\frac{ cotx }{ lnx } \]

  2. LolWolf
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    There's no nice elementary method, other than l'Hospital's. At least, not that I can come up with: \[\begin{align} \lim_{x\to0^+}\left(\frac{\cot x}{\ln x}\right) &= \lim_{x\to0^+}\left(\frac{\frac{d}{dx}\cot x}{\frac{d}{dx}\ln x}\right)=\\\lim_{x\to0^+}\left(\frac{-\csc^2 x}{\frac{1}{x}}\right)&=\lim_{x\to0^+}\left(-x\csc x\right)=-\infty \end{align}\]

  3. Babyslapmafro
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you

  4. LolWolf
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure thing.

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy