## finding limits with square roots in function

Limits, differentiation, related rates, integration, trig integrals, etc.
trdert
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Joined: Tue Aug 04, 2009 1:21 pm
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### finding limits with square roots in function

hi all,

i've got a couple problems i'm working on that require you to find the limit of a function with square roots. i'm having some issues with it. if anyone could lend a hand on the following problem it would be most appreciated:

limx->2 (sqrt(2x)-x)/(x-2)

i know i need to factor out x-2 but i don't know how to do that with the square root in the numerator.

tim

stapel_eliz
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This is an interesting one. I think they're expecting you to multiply by the conjugate of the numerator to get:

. . . . .$\left(\frac{\sqrt{2x}\, -\, x}{x\, -\, 2}\right)\left(\frac{\sqrt{2x}\, +\, x}{\sqrt{2x}\, +\, x}\right)$

. . . . .$\frac{\left(\sqrt{2x}\right)^2\, -\, x^2}{(x\, -\, 2)\left(\sqrt{2x}\, +\, x\right)}$

. . . . .$\frac{2x\, -\, x^2}{-1(2\, -\, x)(\sqrt{2x}\, +\, x)}$

. . . . .$\frac{x(2\, -\, x)}{-1(2\, -\, x)(\sqrt{2x}\, +\, x)}$

Can you see where to go from there?

trdert
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Joined: Tue Aug 04, 2009 1:21 pm
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### Re: finding limits with square roots in function

fantastic, thanks! i'll review the whole multiplying by the conjugate thing also.

nona.m.nona
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### Re: finding limits with square roots in function

The conjugate thing comes up a lot on tests so, yeh, make sure you know it.