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Topic: how to find limit lim (sqrt(x+1) - sqrt(x)
Replies: 6   Last Post: Jun 20, 2012 2:44 AM

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Ben Brink

Posts: 198
From: Rosenberg, TX
Registered: 11/11/06
RE: how to find limit lim (sqrt(x+1) - sqrt(x)
Posted: Jun 20, 2012 2:44 AM
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Ray,
Good work! The technique of "rationalizing the numerator" is not taught in many high schools.
Ben


> Date: Wed, 20 Jun 2012 00:52:41 -0400
> From: discussions@mathforum.org
> To: discretemath@mathforum.org
> Subject: Re: how to find limit lim (sqrt(x+1) - sqrt(x)
>
> lim(x-->?) sqrt(9x^2 + x) - 3x
> = lim(x-->?) [sqrt(9x^2 + x) - 3x] * [sqrt(9x^2 + x) + 3x] / [sqrt(9x^2 + x) + 3x]
> = lim(x-->?) [(9x^2 + x) - (3x)^2] / [sqrt(9x^2 + x) + 3x]
> = lim(x-->?) x / [sqrt(9x^2 + x) + 3x].
>
> Now divide numerator and denominator by x = sqrt(x^2) to get
> lim(x-->?) 1 / [sqrt(9 + 1/x) + 3]
> = 1/(sqrt(9) + 3)
> = 1/6.
>
> I hope this helps!





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