Define f(0,0) in a way that extends f(x, y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.

It cannot be extended.

Step-by-step explanation:

Consider the function . To extend this functions so it is continous at (0,0) we must define . However, this implies that the limit exists. So, we should find if the limit exists or not.

In this case, consider the case in which y =0. When y=0 then

But, when x=0, we get

.

So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.

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step-by-step explanation: