1 point Determine whether each of the following vector fields F is path independent conservative...

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Calculus

1 point Determine whether each of the following vector fields F is path independent conservative or not If it is path independent enter a potential function for it that is a function f x y so that Vf F If it is path dependent enter NONE a If F x y x 2 i 3y 5 then x 2 2 2x 3y 2 2 5y f x y b if F x y 4x 2y i 2x 3y then f x y 2x 2 2xy 3y 2 2 c If F x y 5y 5x then f x y none d If F x y 4x y 2xy then f x y 4x 3 3 xy 2 4x 4y 47 4 In x 4 then e If F x y x 4 f x y 4yln x 4 c 1 if F x y 6y sin xy i 6x sin xy then f x y NONE

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1 point Determine whether each of the following vector fields F is path independent conservative or not If it is path independent enter a potential function for it that is a function f x y so that Vf F If it is path dependent enter NONE a If F x y x 2 i 3y 5 then x 2 2 2x 3y 2 2 5y f x y b if F x y 4x 2y i 2x 3y then f x y 2x 2 2xy 3y 2 2 c If F x y 5y 5x then f x y none d If F x y 4x y 2xy then f x y 4x 3 3 xy 2 4x 4y 47 4 In x 4 then e If F x y x 4 f x y 4yln x 4 c 1 if F x y 6y sin xy i 6x sin xy then f x y NONE