Functions of two variables, continuity

Consider the following functions each of which is defined on the x - y plane

f1(x) = (x-y)/(x+y) if x + y is not 0 and otherwise f1(x,y) = 0

f2(x,y) = (xy)/(x^2 + y^2) if (x,y) is not (0,0) and otherwise f2(0,0) = 0

f3(x,y) = (x^3 - y^3)/(x^2 + y^2) if (x,y) is not (0,0), and otherwise f3(0,0) is 0

Which of these is continuous

A) none B) f1 only C) f2 only D) f3 only E) all three

I know the defination of continuity for a single variable is the lim as x-> a of f(x) = f(a)

So i assume for two variables it should be the lim as (x,y) -> (a,b) of f(x,y) = f(a,b)

But I am not sure how to figure this out can someone help out please

You have the correct definition: if $$U$$ is an open set in $$\mathbb{R}^2$$ and $$(a, b) \in U$$, then $$f: U \to \mathbb{R}$$ is continuous at $$(a, b)$$ if $$\lim_{(x, y) \to (a, b)} f(x, y)$$ exists and equals $$f(a, b)$$.