Prove the theorem: Let f(x, y) be defined in domain D and continuous at the point (x, y1) of D. If f(x1, y1) > 0, then there is a neighborhood of (x1, y1) in which f(x, y) > (x1, y1) > 0. [Hint: Use ϵ = (x1, y1) in the definition of continuity.]
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