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Math Help - L'Hopitals Rule

  1. #1
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    L'Hopitals Rule

    I'm having trouble with this problem. Please help =)

    Lim
    X-> Infinity Ln(lnx) / x


    I know if you plug infinity in there it'll be infinity over infinity and that's when you apply the L'H rule. But when I take the derivative for that it comes out to

    X * 1/lnx * 1/x - Ln(lnX)
    ------------------------
    X^2



    which would equal -infinity / infinity right? But that's not the answer. The answer is 0 but i'm having trouble getting to it. any help will be appreciated. Thanks.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Afterme View Post
    I'm having trouble with this problem. Please help =)

    Lim
    X-> Infinity Ln(lnx) / x


    I know if you plug infinity in there it'll be infinity over infinity and that's when you apply the L'H rule. But when I take the derivative for that it comes out to

    X * 1/lnx * 1/x - Ln(lnX)
    ------------------------
    X^2



    which would equal -infinity / infinity right? But that's not the answer. The answer is 0 but i'm having trouble getting to it. any help will be appreciated. Thanks.

    For L'H rule you dont use the quotient rule.

    \lim_{x \to \infty}\frac{f(x)}{g(x)}=\lim_{x \to \infty}\frac{f'(x)}{g'(x)}

    Take the deriavative of the numerator, then the derivative on the denominator and then take their limits
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  3. #3
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    OMG Thanks alot =)!! I forgot about that little rule haha. THANK YOU VERY MUCHHHHHH!!!
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  4. #4
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    You donīt have to differentiate the entire function, but the dividend and the divisor separately, thatīs what l'hopitalīs rule say.


    If you donīt get the right result tell me and I write it down for you; happens that I suck with latex...
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  5. #5
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    Thanks alot guys but I have another question on another problem. The problem is

    X-> 1
    Lnx / Sin(pi) X

    The answer I got for this was -1 But my teacher got -1/pi. Here's my work

    (1/x) / (sin pi + x * Cos pi)

    If you plug 1 into all the X values you'll end up with 1 / -1 which equals -1 not -1/pi. Did I miss a step?
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  6. #6
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    skeeter's Avatar
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    do you know the chain rule?

    \frac{d}{dx} \sin(\pi x) = \pi \cos(\pi x)
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  7. #7
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    Quote Originally Posted by TheEmptySet View Post
    For L'H rule you dont use the quotient rule.

    \lim_{x \to \infty}\frac{f(x)}{g(x)}=\lim_{x \to \infty}\frac{f'(x)}{g'(x)}

    Take the deriavative of the numerator, then the derivative on the denominator and then take their limits

    Hence the beauty of L'H rule!!
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