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Help with understanding of L'Hospitals Rule

  1. Mar 29, 2012 #1
    1. The problem statement, all variables and given/known data
    This was a question from our lecture notes, just not sure how the prof arrived at the answer.

    lim x->infinity (lnx)^2/x

    2. Relevant equations


    lim x->infinity (lnx)^2/x
    lim x->infinity 2lnx/x

    3. The attempt at a solution


    so both the numerator and denominator are going towards infinity, and by L'H it the lim x->infinity 2lnx/x
    so this means that the numerator is 'growing' faster than the denominator, a constant x? also, how does one arrive at the conclusion that the limit is 0?
     
  2. jcsd
  3. Mar 29, 2012 #2
    (lnx)^2/x = (2/x)(ln x)

    derivative of ln x = 1/x

    Go from there. I'm drunk.
     
  4. Mar 29, 2012 #3
    Just apply L'Hospital's rule again since you are still in an indeterminate inf/inf:
    [tex]\frac{2}{x}[/tex]

    It should now be pretty sensible that it approaches 0 as x approaches infinity.
     
  5. Mar 29, 2012 #4
    RoshanBBQ, thanks! Completely slipped my mind that sometimes we have to apply L'H more than once.
     
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