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Math Help - Calculus 2 limits as x-->0+

  1. #1
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    Calculus 2 limits as x-->0+

    My teacher gave me this problem as an honors problem. She said that at one point I will have to use L'Hopitals rule to solve, but I have no idea where to start.

    1. Evaluate the limit, if it exists.

    l i m (x+1)^cotx
    n-->0+

    Any help would be greatly appreciated
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by JubJub1991 View Post
    My teacher gave me this problem as an honors problem. She said that at one point I will have to use L'Hopitals rule to solve, but I have no idea where to start.

    1. Evaluate the limit, if it exists.

    l i m (x+1)^cotx
    n-->0+

    Any help would be greatly appreciated
    Let  f=x+1 and  g=\cot x .

    We end up with a limit of the form  1^\infty . To fix this notice  \displaystyle f^g = \exp\left(\frac{\ln f}{1/g}\right) .

    So  \displaystyle \lim_{x\to0}f^g = \exp\left(\lim_{x\to0}\frac{\ln f}{1/g}\right) and the limit is of the form  \displaystyle \frac00 (can you see why?).

    Now apply L'Hopital's rule.
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  3. #3
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    I cannot thank you enough! I did not see that it was f raised to the g. My only other question is on the second line you have f^g= exp(ln f/(1/g)). What is the exp part?
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  4. #4
    MHF Contributor chiph588@'s Avatar
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     \exp(x) = e^x
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