F is a function that is f = (x*y^2 - y*x^2 + 3x^3 - y^3)/(x^2 + y^2) if x and y

Question

F is a function that is f = (x*y^2 - y*x^2 + 3x^3 - y^3)/(x^2 + y^2) if x and y are not equal to zero.
If they are, then f = 0.

Calculate fx( 0, 0 ) and fy( 0, 0 ). Fx and Fy are the partial derivatives by x and y.


I can find the partial derivatives, but the problem is that when I plug in x = 0 and y = 0, I get something like
0/0 which simply cannot exist. Does it mean that both Fx and Fy are discontinuous at 0? The limist does not exist at that point? Does that mean that it cannot be evaluated at that point?

Explanation / Answer

If 0/0 exists,then use L'Hospitals rule for calculating the limit,then you can get the answer

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