Help with understanding of L'Hospitals Rule

  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. (lnx)^2/x = (2/x)(ln x)

    derivative of ln x = 1/x

    Go from there. I'm drunk.
  4. Just apply L'Hospital's rule again since you are still in an indeterminate inf/inf:

    It should now be pretty sensible that it approaches 0 as x approaches infinity.
  5. RoshanBBQ, thanks! Completely slipped my mind that sometimes we have to apply L'H more than once.
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Help with understanding of L'Hospitals Rule