Question

What is the limit of `(ln x)^2 / (3x)` as x approaches `oo`?

Answer 1

0

Explanation:

`lim_(x to oo) (ln x)^2 / (3x)`

This is in indeterminate `oo/oo` form so we can use L'Hôpital's Rule

`= lim_(x to oo) (2 (ln x) * 1/x ) / (3) = lim_(x to oo) (2 ln x ) / (3x)`

This is still in indeterminate `oo/oo` form so we can use L'Hôpital's Rule again

`= lim_(x to oo) (2 (1/ x) ) / (3) = lim_(x to oo) (2 ) / (3x) color(red)(= 0)`