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October 5th, 2008, 08:10 PM   #1
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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!!!..
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October 5th, 2008, 08:22 PM   #2
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Re: Math Analysis

You know how to rationalize the denominator, right? Try rationalizing the numerator, that solves this problem.
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October 6th, 2008, 03:48 AM   #3
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Re: Math Analysis

How would that help in this instance?
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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.
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October 24th, 2008, 07:05 AM   #5
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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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