October 5th, 2008, 08:10 PM  #1 
Newbie Joined: Oct 2008 Posts: 2 Thanks: 0  Math Analysis
having trouble on these particular types of problems evaluate lim as x> 0 {(sqrt (x+1))  1}/x ??? any pointers would be greatly appreciated.. This is for my math analysis class...Thanks before hand!!!.. 
October 5th, 2008, 08:22 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Math Analysis
You know how to rationalize the denominator, right? Try rationalizing the numerator, that solves this problem.

October 6th, 2008, 03:48 AM  #3 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Math Analysis
How would that help in this instance?

October 6th, 2008, 05:31 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Math Analysis Quote:
 
October 24th, 2008, 07:05 AM  #5 
Newbie Joined: Oct 2008 Posts: 3 Thanks: 0  Re: Math Analysis
since it becomes 0/0 when 0 is subst. use L'Hospitals rule. the limit exits iff d/dx (num)/d/dx(denom) in your case denom becomes dx/x equals 1 and numerator d/dx((1+x)^(1/2)1 i.e 1/2 srt(1/(1+x)) ) at 0 equal 1/2 hence answer 1/2 

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