Limit of ln as x goes to infinity

[Cacophony]

Homework Statement

lim (lnx)^2/x
x-->infinity

Homework Equations

none

The Attempt at a Solution

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

=5/(x/lnx)

How do I calculate x/lnx?

 

[ehild]

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

 

[Mark44]

Homework Statement

lim (lnx)^2/x
x-->infinity

Homework Equations

none

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.

=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?

 

[checkitagain]

Homework Statement

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}} \ ?