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Math Help - L'Hospital problem

  1. #1
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    L'Hospital problem

    Another one:



    this time im lost
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  2. #2
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    Quote Originally Posted by stiitches View Post
    Another one:



    this time im lost
    From your post title you are obviously aware of how it's to be done. So what have you tried and where are you stuck?
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  3. #3
    Junior Member pirateboy's Avatar
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    Recall, L'Hospital's rule states that if

    \displaystyle \lim_{x\to n}\frac{f(x)}{g(x)} = \frac{0}{0} \;\;\text{or}\;\; \frac{\pm \infty}{\pm \infty}\quad \text{then}\quad \lim_{x\to n} \frac{f(x)}{g(x)} \overset{\text{H}}{=}\lim_{x\to n}\frac{f'(x)}{g'(x)}

    So....

    \displaystyle \lim_{x\to 1}\frac{\ln(x)}{\sin(2\pi x)}\overset{\text{H}}{=}\lim_{x\to 1}\frac{\frac{d}{dx}\ln(x)}{\frac{d}{dx}\sin(2\pi x)}

    I'm confident you can handle it from here.
    Last edited by pirateboy; November 4th 2010 at 09:55 PM. Reason: said too much
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  4. #4
    Junior Member pirateboy's Avatar
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    oops! i left our a few conditions. f\;\text{and}\;g must be differentiable and  g'(x) \neq 0.

    But both are true here. So it shouldn't matter. Just bust out some sweet differentiation moves and you're golden.
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