limit of Ln: whats the limit of (lnx)^2/x when x approaches infinity ?

Question

with use of l'hospital ,it's 2lnx/x and sencond l'hospital 2/x and as x goes to infinity then it's zero ?!!!

Answer 1

The limit is 0
Use L´Hôpital
= lim 2lnx /x = lim2/x=0

Answer 2

when a limit problem approaches a value of infinity/infinity as the variable approaches infinity, you apply L'hopital's (bad spelling) rule and take the derivitives of both the numerator and denominators [*not* the expression], then re-evaluate as the variable approches infinity. In this case, the derivitive 2*ln(x)/x still approaches infinity, so apply the rule again to obtain: 2/x, whose limit is 0.