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Limits and Continuity for Multivariate Functions

Limits and Continuity for Multivariate Functions

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Given a function of two variables f : D !R, D R2 such that D contains points arbitrarily close to a point (a;b), we say that the limit of f(x;y) as (x;y) approaches (a;b) exists and has value L if and only if for every real number ">0 there exists a real number >0 such that

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