Function, using two-path test, finding limits

gap0063

f(x,y)=(x)/ (1-y²), y does not equal 1 or -1

Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R², and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.


I really don't know where to begin...
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

csopi

For the existence of such g it is necesarry that lim (x->x0, y->1) f(x,y)=A(x0,1) exist and depend only on x0 (and not on the path). But in our case it does not hold:

Calculate the limit for x0=0 for two different paths:
1. y=x+1 (x->0)
2. y=2x+1 (x->0)

You wont get the same result, so such g does NOT exist.

zetmaths

how do i choose the equations of lines c and d,to find limits along when finding limits by two parts