Prove that the limit of function f(x,y)=(x+y^2)/(x^2-y) exists if (x,y) approach to (0,0).

The given function f(x,y) = (x + y^2) / (x^2 - y), has two
independent variables. If the limit for the function f(x, y) approaching (0, 0) is
defined, we should get the same value whether we take the values of (x, y) along x = 0,
or (x, y) along y = 0.

If we follow x =
0

lim y--> 0 [ (y^2) / (- y) ] =
-y

If we follow y = 0

lim
x--> 0[ x/ x^2] = 1/x

This shows that the value of
the function as (x,y) approach (0,0) is not the
same.

The limit of the function at (0,0) does
not exist.