Determine if a function is continuous in points
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Determine if a function $f(x, y)$ is continuous in points (1, 1) and (0, 0). $$f(x, y) = begin{cases} frac{x^2+2xy-3y^2}{x^3-y^3}, & x neq y \ A, &x=y=0 \ B, & x =y= 1end{cases}$$ I do struggle with conclusions. How to approach it? I suppose, now one should find the iterated limits, if multivariable limit and iterated limits are equal in the point $M(x_0, y_0)$ , therefore, the function is continuous in $M$ (it requires clarification, as well. I am not sure if it's viable to state so). $$1) lim_{yto1}lim_{xto1}frac{x^2+2xy-3y^2}{x^3-y^3} = lim_{yto1}frac{1+2y-3y^2}{1-y^3} = lim_{yto1}frac{3(y-1)(y+frac{1}{3})}{(y-1)(y^2+y+1)} = frac{4}{3}$$ $$2) lim_{xto1}lim_{yto1}frac{x^2+2xy-3y^2}{x^3-y^3} = lim_{xto1}frac{x^2+2x-3}{x^3-1} = lim_{xto1}frac{(x-1)(x+3)}{(x-1)(x^2+x+1)} = fra