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Determine which of the following vector fields F in the plane is the gradient of a...

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Question

Basic Math

Determine which of the following vector fieldsF in the plane is the gradient of a scalarfunction f. If such an f exists, find it. (If ananswer does not exist, enter DNE.)

F(x, y) = 3xi + 3yj

f(x, y) =

F(x, y) = 6xyi + 6xyj

f(x, y) =  

F(x, y) = (4x2 + 4y2)i + 8xyj

f(x, y) =

  

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