Verified answer

Multiply by (2-√x) / (2-√x)

(2+√x) (2-√x) / (2-√x) (2-√x) ----- (1)

The numerator is of form (a+b)(a-b) = a^2-b^2

a=2

b= √x

a^2-b^2 = 4-x

(1) becomes:

(4-x) / (2-√x)^2

= x(4/x-1) / x(2/√x -1)^2

= (4/x-1) / (2/√x -1)^2 --- (2)

lim x-->∞ 4/x=0

lim x-->∞ 2/√x =0

(2) becomes:

-1/(-1)^2 = -1

The limit is -1

-1

divide every term by root x so that terms 2/root x converge to zero, while the root over root is 1 so that 1/-1 = -1

hi :)

without de l'hopital:

http://www.xlogx.com/en/limit-of-a-function/26b88d...

Hope this helps! Bye!