# Limit of ln as x goes to infinity

by Cacophony
Tags: infinity, limit
 P: 41 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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Thanks
P: 10,767
 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
P: 21,397
 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?

P: 99
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

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

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