Let A =R^2 - {(0,0)} and B = {(x,y); abs y < x^2}. Define filterbasesA= {A intersection B_e(0,0): e>0} andB= {B intersection B_e(0,0): e>0}. Defind f on A by f(x,y) = (x^2-y^2)/(x^2 + y^2). Prove that the limit of f alongAdoes not exist, but the limit of f alongBdoes.

Thanks.