Physics Forums

Physics Forums (http://www.physicsforums.com/index.php)
-   Calculus & Beyond Homework (http://www.physicsforums.com/forumdisplay.php?f=156)
-   -   Help with understanding of L'Hospitals Rule (http://www.physicsforums.com/showthread.php?t=591388)

shocklightnin Mar29-12 01:27 AM

Help with understanding of L'Hospitals Rule
 
1. The problem statement, all variables and given/known data
This was a question from our lecture notes, just not sure how the prof arrived at the answer.

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

2. Relevant equations


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

3. The attempt at a solution


so both the numerator and denominator are going towards infinity, and by L'H it the lim x->infinity 2lnx/x
so this means that the numerator is 'growing' faster than the denominator, a constant x? also, how does one arrive at the conclusion that the limit is 0?

tazzzdo Mar29-12 01:57 AM

Re: Help with understanding of L'Hospitals Rule
 
(lnx)^2/x = (2/x)(ln x)

derivative of ln x = 1/x

Go from there. I'm drunk.

RoshanBBQ Mar29-12 02:20 AM

Re: Help with understanding of L'Hospitals Rule
 
Quote:

Quote by shocklightnin (Post 3839528)
1. The problem statement, all variables and given/known data
This was a question from our lecture notes, just not sure how the prof arrived at the answer.

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

2. Relevant equations


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

3. The attempt at a solution


so both the numerator and denominator are going towards infinity, and by L'H it the lim x->infinity 2lnx/x
so this means that the numerator is 'growing' faster than the denominator, a constant x? also, how does one arrive at the conclusion that the limit is 0?

Just apply L'Hospital's rule again since you are still in an indeterminate inf/inf:
[tex]\frac{2}{x}[/tex]

It should now be pretty sensible that it approaches 0 as x approaches infinity.

shocklightnin Mar29-12 03:27 PM

Re: Help with understanding of L'Hospitals Rule
 
RoshanBBQ, thanks! Completely slipped my mind that sometimes we have to apply L'H more than once.


All times are GMT -5. The time now is 10:24 AM.

Powered by vBulletin Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums