## anonymous 4 years ago evaluate the limit algebraically... lim x-->2 (x-2)/(sqrt(x)-sqrt(4-x))

1. anonymous

$\lim_{x\rightarrow 2}\frac{x-2}{\sqrt{x}-\sqrt{4-x}}$ like that?

2. anonymous

first make sure that, if you replace x by 2, you get 0/0, which you do. then multiply numerator and denominator by the conjugate of the denominator, i.e. multiply by $\frac{\sqrt{x}+\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}$

3. anonymous

your new denominator will be $2x-4=2(x-2)$ so you can cancel with the $x-2$ in the numerator, leaving only $\frac{\sqrt{x}+\sqrt{4-x}}{2}$ and now replace x by 2

4. anonymous

and don't kick out farmdawg, he doesn't like it

5. anonymous

haha what about a farmdawg? other than that thank you...