Have you attempted doing these limits? Take certain paths and determine whether the limits are the same or not; if not, then there is a contradiction and the limit D.N.E., and if it does then you can use approximating methods to determine whether it is a limit. Note that even if you find 3 paths with the same limit, this does not necessarily mean that the limit exists. You have to prove it. To show this, consider the 'squeeze principle':

|f(x,y) - L| ...