It suffices to show the exponent of base r is negative when a + b < 2? Do I need to examine other paths as approaches to evaluate the limit? Since the polar coordinate substitution seems to encompass more general cases, would I still need the a + 2b > 0 from the parabola path though?
Also...
Homework Statement
Find all real a and b such that the limit \lim_{(x,y) \to (0,0)} \frac{\left\vert x \right\vert ^a \left\vert y \right\vert ^b}{x^2+y^2} exists and is finite. (Hint: it is not enough to find the limit or prove it exists in the region found. You must also prove that the limit...