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 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: 938 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
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Re: Math Analysis

Quote:
 Originally Posted by cknapp How would that help in this instance?
It removes the singularity... once you do that (and simplify) you just substitute x = 0 and you're done.

 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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