8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the pla...
(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis CirculationF dr- (1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis CirculationF dr-
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F around a circle C of radius 0.1, centered at the origin, if C is on the ry- yz-, and rz-plane respectively oriented counter-clockwise when viewed from the positive z, positive a, and positive y-axis respectively 7. Three small squares Ci,C2, Cs each with sides 0.1, centered at the...
6. (4 pts) Vectors VÀ and VB generate a square in the plane x +2y + 3z = 1, as shown in the left figure. A smooth vector field F in the square behaves as shown in the right figure. В ID 18 12 10 0 B 10 14 16 18 А Assume that the greatest circulation density of T at P is 5 and at Q is 2. (a) Find curl at P. (b) Find curlī at Q. (c)...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
please help ! Q1-Q6 1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r +...