## anonymous one year ago find the limit http://www.imagebam.com/image/cb7f41432921593

1. misty1212

HI!!

2. freckles

oooo oo rationalize the numerator! :)

3. misty1212

gimmick is to multiply top and bottom by the conjugate of the numerator, in other words compute $\frac{\sqrt{2-x}-\sqrt{x}}{x-1}\times \frac{\sqrt{2-x}+\sqrt{x}}{\sqrt{2-x}+\sqrt{x}}$

4. misty1212

leave the denominator in factored form

5. Loser66

Why not l'hospital?

6. freckles

you can do that as well since you have 0/0 when you plug in x=1 I think the algebra is cute and cuddly though

7. Loser66

:)

8. misty1212

my guess is that this is a pre-l'hopital question also the derivative will be butt ugly