9(a) (1 point) Consider the vector field F (x, y, z) (2z + 5y) i+ (4z...

 

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9(a) (1 point) Consider the vector field F (x, y, z) (2z + 5y) i+ (4z + 5x)j+ (4y + 2x) k. a) Find a function f such that F = Vf and f(o, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0, 0) to (1, 1, 1). Use part a) to compute the line integral F dr. (b) (1 point) Suppose Vf(x, y) = 2y sin(xy)i + 2x sin(xy)j. F Vf(x, y), and C is the segment of the parabola y 2x2 from the point (3, 18) to (5, 50). Then %3D -dr = (c) (1 point) If F = V(5x2 + 3y), find F dr where C is the quarter of the circle x + y = 4 in the first quadrant, oriented counterclockwise. SeF dr = 9(a) (1 point) Consider the vector field F (x, y, z) (2z + 5y) i+ (4z + 5x)j+ (4y + 2x) k. a) Find a function f such that F = Vf and f(o, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0, 0) to (1, 1, 1). Use part a) to compute the line integral F dr. (b) (1 point) Suppose Vf(x, y) = 2y sin(xy)i + 2x sin(xy)j. F Vf(x, y), and C is the segment of the parabola y 2x2 from the point (3, 18) to (5, 50). Then %3D -dr = (c) (1 point) If F = V(5x2 + 3y), find F dr where C is the quarter of the circle x + y = 4 in the first quadrant, oriented counterclockwise. SeF dr =