$\displaystyle f(x,y) = \frac{x}

{{1 - {y^2}}},y \ne \pm 1

$

a) Using the paths x=0 and y=x+1, show by the two-path test that the limit, $\displaystyle {\lim _{(x,y) \to (0,1)}}f(x,y)

$ does not exist.

b) Find the limit, $\displaystyle {\lim _{(x,y) \to (1,0)}}f(x,y)

$, if it exists. IF it does not, explain why not.

c) Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R^2, 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 not.

I'm not sure where to start for a)

for b) i think its $\displaystyle {\lim _{(x,y) \to (0,1)}}\frac{x}

{{1 - {y^2}}} = \frac{1}

{{1 - {{(0)}^2}}} = 1

$

and I also don't know where to start for c)