Answer: We have seen that all vector fields of the form satisfy the equation and that

Chapter 16, Problem 39

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We have seen that all vector fields of the form satisfy the equation and that all vector fields of the form satisfy the equation (assuming continuity of the appropriate partial derivatives). This suggests the question: Are there any equations that all functions of the F t curl F 0 F curl G div F 0 form must satisfy? Show that the answer to this question is No by proving that every continuous function on is the divergence of some vector field. [Hint: Let ,where f div G f 3 Gx, y, z tx, y, z, 0, 0 tx, y, z xx 0 f t, y, z dt.] So far we have