Question

If $\lim_{(x,y) \to (a,b) f(x,y)=L$, and if the one dimensional limits $\lim_{x \to a} f(x,y)$ and $\lim_{y \to b} f(x,y)$ both exist, prove that $\lim_{x \to a} [ \lim_{y\to b} f(x,y) ] = \lim_{y \to b} [ \lim_{x\to a} f(x,y) ] =L$ .

Answer 1

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