Question

find the limit
http://www.imagebam.com/image/cb7f41432921593

Answer 1

HI!!

Answer 2

oooo oo rationalize the numerator! :)

Answer 3

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

Answer 4

leave the denominator in factored form

Answer 5

Why not l'hospital?

Answer 6

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

Answer 7

:)

Answer 8

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