how to find the mininum of k to make f(x,y) = lxl^k*lyl^k/(x^2+y^2) convergent?

in practice book, there is a question which is similar but simple than this one, like xy/(x^2+y^2) is convergent or not, i know this is not convergent, as when keep y constant, if y=x, lim(x->0)=1/2, while if y=0, lim(x->0)=0, so it is not convergent.

what about this one? tks in advance!