## finding limits with square roots in function

Limits, differentiation, related rates, integration, trig integrals, etc.

### 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
trdert

Posts: 6
Joined: Tue Aug 04, 2009 1:21 pm

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?

stapel_eliz

Posts: 1729
Joined: Mon Dec 08, 2008 4:22 pm

### Re: finding limits with square roots in function

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

Posts: 6
Joined: Tue Aug 04, 2009 1:21 pm

### Re: finding limits with square roots in function

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

Posts: 256
Joined: Sun Dec 14, 2008 11:07 pm