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August 20th, 2009, 11:11 AM  #1 
Newbie Joined: Jul 2009 Posts: 7 Thanks: 0  limit to infinity of ln n / ln (n+1)
I'm trying to figure out how to find the limit of ln n / ln(n+1) as n approaches infinity. The answer booklet says it's 1. How do I approach this?

August 20th, 2009, 11:32 AM  #2 
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0 
Are you allowed to use l"Hospital's Rule?

August 20th, 2009, 11:55 AM  #3 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: limit to infinity of ln n / ln (n+1)
Use 
August 20th, 2009, 06:12 PM  #4 
Newbie Joined: Jul 2009 Posts: 7 Thanks: 0  Re: limit to infinity of ln n / ln (n+1)
Thanks for the replies. Yes I looked at the rule I can use it. I just have another question what is the derivative of f(x) = ln (x+1)? Do I let u = x + 1, then multiply the derivative of f(x) with the derivative of u?

August 20th, 2009, 10:19 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041 
You multiply the derivative of f(u) with respect to u by the derivative of u with respect to x and then replace u with x + 1.

August 21st, 2009, 05:59 AM  #6 
Newbie Joined: Jul 2009 Posts: 7 Thanks: 0  Re: limit to infinity of ln n / ln (n+1)
Once I use the rule I'll end up with (x + 1) / x. Do I just divide each literal by x?

August 21st, 2009, 10:17 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041 
Yes.


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