Exercise Problem

Exercise. Let F (x, y) = ({,{! ). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) = ?Exercise. Let F (x, y) = (6 xy, 3x2 ). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =Exercise. Let F (x, y) = ,). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) = ?Exercise. Let F (x, y) = (1, 2 y ). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =Exercise. Let F (x, y) = (3, 2 y ). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =Exercise. Let F (x, y) = (6xy2 -4y, 6xy -4x ). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =Exercise. Let F (x, y) = (-8 xy-4, -4x2 ). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. You should use the Clairaut gradient test. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =Exercise. Let F (x, y) = (-2, -2). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. Reveal Hint F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =Exercise. Let F (x, y) = (, (:). Identify whether F is a gradient field, and if it is, find a potential function F such that F(0, 0) = 0. F is a gradient field. F is not a gradient field. Correct Exercise. A potential function F such that F(0, 0) = 0 is: F(x, y) =