How do I evaluate the limit as t -> 2 of: (sqrt(t+2)-2)/t-2

BTW the answer is NOT 0

If you plug in 2, you get 0/0, so that is indeterminate. So, we can apply L'hopitals rule by taking the derivative of the numerator and the denominator to get
lim t->2 (1/2*(t+2)^(-1/2) / 1 ) = 1/2*(4)^(-1/2) = 1/(2*2) = 1/4

http://www.wolframalpha.com/input/?i=lim…

first you TRY to just insert value t=2....
if you get something like zero/zero or infinity/infinity then you can (and must) use L'Hopithal rule
which says differentiate numerator and denominator separately and try again