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Question 1. Let C be the intersection of the plane -2r +5y with the cylinder r2+y2=...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axi...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find the work done by the force field F= (y2/2, Z, x) in moving a particle...
Find the work done by the force field F= (y2/2, Z, x) in moving a particle along the curve C, where C is the intersection curve of the plane x +z = 1 and the ellipsoid x2 + 2y2 + x2 = 1 oriented counterclockwise when viewed from positive z— axis.
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of th...
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find...
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your...
1. Let C denote the closed curve of intersection of the hemisphere z = (25 –...
1. Let C denote the closed curve of intersection of the hemisphere z = (25 – x’ - y²); and the cylinder x² + y? = 9 oriented counterclockwise. Compute fF.ds where F =(-y,x,z).
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that li...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e...
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
please show all work Use Stokes' Theorem to evaluate Sc F. dr where C is oriented...
please show all work
Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz ,...
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 an...
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?) is a given vector field. Find the circulation F dr
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?)...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find the work done by the force field F= (y2/2, Z, x) in moving a particle along the curve C, where C is the intersection curve of the plane x +z = 1 and the ellipsoid x2 + 2y2 + x2 = 1 oriented counterclockwise when viewed from positive z— axis.
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
1. Let C denote the closed curve of intersection of the hemisphere z = (25 – x’ - y²); and the cylinder x² + y? = 9 oriented counterclockwise. Compute fF.ds where F =(-y,x,z).
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
please show all work
Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?) is a given vector field. Find the circulation F dr
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?)...
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