problem 1:
evaluating the lim as x--> infinity gives you infinity/infinity, so use L'Hospital's rule, which tells you to take the derivative of the numerator and denominator. This gives you
Lim 1 / (1/2 (x-2)^-(1/2)), which simplifies to:
Lim 2sqrt(x-2) as x --->infinity
you can now evaluate the lim, which gives you lim = infinity
problem 2:
evaluating the lim as x-->2+ gives you Lim 2/0, which is undefined
therefore, there is a vertical assympote at x = 2
I forgot how to determine if the lim approaches + or - infinity, so I suggest just graphing it.