help with limit expression?

Question

lim (x,y) --> (3,2) ((y-2)^2)ln(y-1) / ((x-3)^2)+((y-2)^2)

use any two paths that pass through (3,2) to guess what the limit may be

Answer 1

The two obvious paths to choose are the one keeping x constant and the one keeping y constant. So:

1. setting x = 3, what is the limit as y goes to 2 of the given expression?

2. setting y = 2, what is the limit as x goes to 3 of the given expression?

If the two limits are the same, that'd be a pretty good guess, don't you think?

Keep in mind that f(x)/f(x) = 1, even if f(x) = 0.
http://en.wikipedia.org/wiki/Indeterminate_form