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) = (-12x - 2y)i + (-2x + 6y)j f(x, y) = F (x, y) = -6yi - 5xj f(x, y) = F (x, y, z) = -6xi - 5yj + k f ( x , y , z ) = F (x, y) = -6 sin y)i + (-4y - 6x cos y)j f(x, y) = F (x, y, z) = -6x2i - 2y2j + 3 z2k f (x, y, z ) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

Explanation / Answer

A.N B.N C. f(x,y)=-3x^2-2.5y^2+z+a where a is constant D. f(x,y)=-6xsiny-2y^2+a where a is constant E. f(x,y,z)=-2x^3-(2/3)y^3+z^3+a where a is constant

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