Let Prove or disprove that there is a a vector-valued function F(x, y, z) = (M(x, y,
Question:
Let
Prove or disprove that there is a a vector-valued function F(x, y, z) = (M(x, y, z), N(x, y, z), P(x, y, z)) with the following properties:
(i) M, N, P have continuous partial derivatives for all
(x, y, z) ≠ (0, 0, 0);
(ii) Curl F = 0 for all (x, y, z) ≠ (0, 0, 0);
(iii) F(x, y, 0) = G(x, y).
Transcribed Image Text:
G(x, y) = 2. 0). -y X x² + 4y²² x² + 4y²⁹
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