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Therefore, F = 〈 g y, − g x 〉 F = 〈 g y, − g x 〉 and div F = g y x − g x y = 0 div F = g y x − g x y = 0 by Clairaut’s theorem The converse of Divergence of a SourceFree Vector Field is true on simply connected regions, but the proof is too technical to include here Thus, we have the following theorem, which can test.

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