I find that the best way of evaluating (non obvious) limits of multivariable functions is by using polar coords. First (if necessary) convert or reassign the function so that at the limit point, the variables all tend to 0 and than sub in x=rcos(angle), y=rsin(angle) where angle is arbitary. Than let x,y->0 as r->0. This way the limit if it exists will be found everytime because the arbitary angle will mean that graphs could come in at all possible way. Other ways of evluating these limits involving rearranging the function and than apply the Sandwich theorm or other ones to find the limit. Or sub different functions as they near the limit point such as linear, quadratic, hyperbola etc. These ways all involve a number of steps and involve so much extra work and guess work. Polar coordinates seem to solve the problem in one go. My Uni does not teach the polar coords way but the latter ways which is strange to me.