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Using L'Hospital's rule with roots and log functions

  1. Oct 7, 2008 #1
    Can someone help me use L'HOP to determine

    lim x -> 0 [ [tex]\sqrt{x}[/tex]*ln(x) ]

    ??? I'm confused!!
     
  2. jcsd
  3. Oct 7, 2008 #2

    Hootenanny

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    Re: L'hop

    L'Hopital's rule doesn't apply here. One can only apply L'Hopital's rule for a limit of a quotient and only then when the limit is undefined.
     
  4. Oct 7, 2008 #3

    Dick

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    Re: L'hop

    Write it as ln(x)/x^(-1/2). Now it's a quotient and infinity/infinity. Looks good for l'hop.
     
  5. Oct 7, 2008 #4

    Hootenanny

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    Re: L'hop

    *Hangs head in shame and shuffles back into the Physics section*
     
  6. Oct 7, 2008 #5
    Re: L'hop

    why can i rewrite x^(1/2) as x^(-1/2) ??? I don't understand.
     
  7. Oct 7, 2008 #6

    cristo

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    Re: L'hop

    You can't, but you can write [tex]x^{1/2}[/tex] as [tex]\frac{1}{x^{-1/2}}[/tex], which is what Dick has done above.
     
  8. Oct 7, 2008 #7

    Hootenanny

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    Re: L'hop

    You can't rewrite x^(1/2) as x^(-1/2), but you can rewrite it as,

    [tex]x^{1/2} = \frac{1}{x^{-1/2}}[/tex]

    as Dick suggests.

    Edit: Get out of my head cristo :tongue2:
     
  9. Oct 7, 2008 #8

    cristo

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    Re: L'hop

    :wink:
     
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