Question

evaluate the limit algebraically...
lim x-->2 (x-2)/(sqrt(x)-sqrt(4-x))

Answer 1

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

Answer 2

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
\[\frac{\sqrt{x}+\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}\]

Answer 3

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

Answer 4

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

Answer 5

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