HINT
HINT: We have two approaches for such limits.
You can try using polar coordinates and see if
f(x,y) tends to 0 as r tends to zero. If not,
try taking limits along different paths to the
origin to show that the limit cannot exist.
 
ANSWER
ANSWER: No, the limit as one approaches the origin along
the x-axis (or along the y-axis) is 0. The limit as one
approaches the origin along the line y = x is 1/2. Since
these are not equal, the limit posed does not exist.