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 Quote by shocklightnin 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?
Just apply L'Hospital's rule again since you are still in an indeterminate inf/inf:
$$\frac{2}{x}$$

It should now be pretty sensible that it approaches 0 as x approaches infinity.