Evaluating limits????

Question

Hey, not sure how to solve the following limit

http://img299.imageshack.us/img299/3605/limrs9.jpg

explanation would be helpful, ty

Answer 1

multiply top and bottom by sqrt x+sqrt 2

and you;ll see and cancellation.

Your answer should be

2 times sqrt 2

Answer 2

the limit is zero.

when taking the limits of fractions you must first make sure that the denominator does not approach zero.  that would make the top (if a real limit) approach + or - infinity.  that is not the case here so lets look at the numerator

lim as x apporaches 2 of (x-2).  first you can get to two in two ways.  counting up or down.  counting up (1.1, 1.2, 1.3, etc) you see that the limit approaches zero.  counting down it does as well.  since it goes to the same number from both sides the limit exists and is approaching zero.

Answer 3

(x-2)/(sqrtx - sqrt2) =

(x-2)*(sqrtx- sqrt2) / (x-2) =

sqrtx + sqrt2

Lim x --> 2

sqrt2 + sqrt2 = 2sqrt(2)

lmit is 2sqrt2