Question

is \[\lim_{x\rightarrow 0}\lim_{y\rightarrow 0}f(x,y) =\lim_{y\rightarrow 0}\lim_{x\rightarrow 0}f(x,y)\]?

Answer 1

You know the answer already, right? No, not necessarily. Now give us a counterexample.

Answer 2

Still waiting for your example of a function f that has the property that the two limits are not equal.