
Question 1 5 pts True or False. The vector field F(x, y) = {xy i +...
Is the below statement True or False? The vector field F(x,y) =<xy?, x?y) is conservative. True False
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
7.) (12 pts.) Verify Green's Theroem 2 for the Vector Field F(x, y) = (xy)i + (y?)3, where the closed curve C is the circle x² + y2 = 1.
The vector field + (x,y) = (ycos (xy) + 2e*, xcos(xy) + 2ycos (y2)) is conservative. Find f(x,y) such that F = Of. f=sin(x?y) + ye* + 2ys in (y? a. f = 2sin(xy) +2e* + sin(y? O b. 2 f=sin(xy) +2e* + sin(y?) OC f=sin(x+y) + 2ye* + sin(y) O d. sin (2) f=sin(x) + 2ye* + e. 2
Find the work done by the vector field F(x, y) = {xy i + áraj (the vector field from Question 1) on a particle that moves from (0,0) to (0, 1) (moving in a straight line up and along the y axis) and then from (0, 1) to (3, 2) along the curvey= Vx+1. Thus the path is given by along the curve y=x+1 (0,0) up the y-axis + (0,1) (3,2) 1 F. dr 2 F. dr = 0 18...
(9 marks) QUESTION 4 a) Given vector field Éx,y,z) --yº coszi - 3xy cosz j+ xy" sinzk. Show that F is a conservative vector field. (4 marks) ii) Find the potential function, f such that F=Vf. (4 marks)
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
Please describe the contour map and list important aspects of
it, thanks!
Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x, y) for which f(x, y) is a potential function, b) c) sketch a contour map of f (x, y) and, on the same figure, sketch F(x,y) (on R2). Comment on any important aspects of your sketch.
Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x,...
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.