Determine the following limit, or show it doesn't exist.
lim [(x,y) -> (1,0)] [2(x - 1)*y^(3/2)]/[x^2 - 2x + 1 + y^3]
So I tried several paths.
Along x = 1, we have:
lim [(1,y) -> (1,0)] [2(0)y^(3/2)]/y^3 = 0/y^3 = 0
Along y = 0, we have:
lim [(x,0) -> (1,0)] 0/[x^2 - 2x + 1] = 0
So, it *appears* the limit exists so far, but in reality it exists until you can prove otherwise, that is, find a path that does not = 0. If it does exist, how do I show that it exists (and there is, in fact, NOT a path out there that does not = 0).