For each of the following vector fields F , decide whether it is conservative or

Question

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, f = F). If it is not conservative, type N. F (x, y) = (-16x + 6y) i + (6x + 8y) j f(x, y) = F (x, y) = -8yi - 7xj f (x, y) = F (x, y, z) = -8xi - 7yj + k f(x, y, z) = F(x .y) = (-8sin y)i + (12y - 8x cos y)j f(x, y) =| F (x, y, z) = -8x2i + 6y2j + 4z2k f (x, y, z) = Note: Your answers should be either expressions of x: y and z (e.g. "3xy + 2yz")r or the letter "N"

Explanation / Answer

A. f(x,y) = -8x^2 + 6xy + 4y^2 B. N C. f(x,y,z) = -4x^2 - 7/2 y^2 + z D. f(x,y) = -8x sin(y) + 6y^2 E. f(x,y,z) = -8/3 x^3 + 2y^3 + 4/3 z^3

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