Consider $f(x,y) = x^2+y^2$ when $x-y \neq 0$ and $0$ if $(x,y) = (0,0)$.
This function is easily shown to be continuous along all paths, but along $x=y$ it is not defined!
So will it said to be continuous at $0,0$ ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community