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Necessary and sufficient conditions for the existence of limits of the form lim(x,y)→(a,b)f(x,y)/g(x,y) are given, under the hypothesis that f and g are real analytic functions near the point (a,b), and g has an isolated zero at (a,b). The given criterion uses a constructive version of Henselʼs Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials...
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