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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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Cool Jessica

Posts: 6
From: Irving, TX
Registered: 4/23/12
Re: how to find limit lim (sqrt(x+1) - sqrt(x)
Posted: Jun 20, 2012 12:52 AM
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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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