## limit of ln as x goes to infinity

1. The problem statement, all variables and given/known data
lim (lnx)^2/x
x-->infinity

2. Relevant equations

none

3. The attempt at a solution

=5lnx/x * (1/lnx)/(1/lnx)

=5/(x/lnx)

How do I calculate x/lnx?
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 Quote by Cacophony 3. The attempt at a solution =5lnx/x * (1/lnx)/(1/lnx) =5/(x/lnx) How do I calculate x/lnx?
I do not follow you. What have you done?

ehild

Mentor
 Quote by Cacophony 1. The problem statement, all variables and given/known data lim (lnx)^2/x x-->infinity 2. Relevant equations none 3. The attempt at a solution =5lnx/x * (1/lnx)/(1/lnx)
Where did the 5 come from? In fact, where did any of this come from? What you have makes zero sense to me.

Also, since you haven't taken the limit yet, you should not get rid of the "lim" symbol.
 Quote by Cacophony =5/(x/lnx) How do I calculate x/lnx?
This is a problem that is suited to L'Hopital's Rule. Have you covered it yet?

## limit of ln as x goes to infinity

 Quote by Cacophony 1. The problem statement, all variables and given/known data lim (lnx)^2/x x-->infinity
Cacophony,

what you typed is equivalent to:

$$\displaystyle \lim_{x\to \infty}\dfrac{[ln(x)]^2}{x}$$

Did you intend

$$\displaystyle \lim_{x\to \infty}[ln(x)]^{\frac{2}{x}} \ ?$$