f(x.y) =0 (x=0,y>=0) in the 1st quadrant
=-x (x>=0,y(0-,0-) limit f(x,y) = 0
(x,y)->(0+,0+) limit f(x,y) = 0
(x,y)->(0-,0+) limit f(x,y) = 0
(x,y)->(0+,0-) limit f(x,y) = 0
f(0,0)=0
Therefore,the function f(x.y) is continuous at the point (0,0),and all the other points in the region of R².
∂f/∂x = 0 (x=0,y>=0)
= -1 (x>=0,y=0)
= 0 (x>=0,y