Let (x, y) = xy/(x 2 + y 2 ). Show that (x, y) approaches zero along the x- and y-axes. Then prove that does

Let ƒ(x, y) = xy/(x² + y²). Show that ƒ(x, y) approaches zero along the x- and y-axes. Then prove that  does not exist by showing that the limit along the line y = x is nonzero.

lim f(x,y) (x,y) (0,0)