Let F(x, y, z)= (3x²y, x³ + 4y³,0) be a vector field on R³. a) Is there a scalar field f such that Vf = F? b) If so, find such an f; if not, explain why no such f exists.

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scalar field

1) Let F(x, y, z) = (3x2y, x3 + 4y3,0) be a vector field on R³.
a) Is there a scalar field f such that Vf = F?
b) If so, find such an f; if not, explain why no such f exists.
Transcribed Image Text:1) Let F(x, y, z) = (3x2y, x3 + 4y3,0) be a vector field on R³. a) Is there a scalar field f such that Vf = F? b) If so, find such an f; if not, explain why no such f exists.
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