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    Implicit Function Theorem

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    Determine whether the equation xyz + sin(x + y + z) = 0 can be solved for z in a nonempty, open set V containing the point (x, y, z) = (0, 0, 0). If it can, is the solution differentiable near the point (x, y) = (0, 0)?

    See the attached file. Solution to 11.6.2(a) is needed.

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    Solution Summary

    A complete, detailed solution of the given problem (including statements of the pertinent definitions and a statement of the pertinent version of the Implicit Function Theorem) is provided.