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Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y²...
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where...
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i...
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i + (-2)5+(z)k, where Surface S is that portion of the paraboloid z= 6 – 12 – yº, which lies above the plane z = 2.
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral...
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
11.) (19 pts.) Verify the Divergence Theorem for F(q, y, z) = (y)i + (-2) 3...
11.) (19 pts.) Verify the Divergence Theorem for F(q, y, z) = (y)i + (-2) 3 + (22) ł, where the solid D is enclosed by the paraboloid z = 22 + y2 and the plane z = 1.
Verify Stokes, Theorem for the surface S that is the paraboloid given by z = 6-x2-y2 that lies ab...
Verify Stokes, Theorem for the surface S that is the paraboloid given by z = 6-x2-y2 that lies above the plane z 2 (oriented upward) and the vector field F(x, y, z)2yzi+yj+3xk.
Verify Stokes, Theorem for the surface S that is the paraboloid given by z = 6-x2-y2 that lies above the plane z 2 (oriented upward) and the vector field F(x, y, z)2yzi+yj+3xk.
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
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...
b) Verify the Stokes' theorem where F = (2x - y)i + (x +z)j + (3x...
b) Verify the Stokes' theorem where F = (2x - y)i + (x +z)j + (3x – 2y)k and S is the part of z = 5 – x2 - y2 above the plane z = 1. Assume that S is oriented upwards.
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i + (-2)5+(z)k, where Surface S is that portion of the paraboloid z= 6 – 12 – yº, which lies above the plane z = 2.
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
11.) (19 pts.) Verify the Divergence Theorem for F(q, y, z) = (y)i + (-2) 3 + (22) ł, where the solid D is enclosed by the paraboloid z = 22 + y2 and the plane z = 1.
Verify Stokes, Theorem for the surface S that is the paraboloid given by z = 6-x2-y2 that lies above the plane z 2 (oriented upward) and the vector field F(x, y, z)2yzi+yj+3xk.
Verify Stokes, Theorem for the surface S that is the paraboloid given by z = 6-x2-y2 that lies above the plane z 2 (oriented upward) and the vector field F(x, y, z)2yzi+yj+3xk.
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
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...
b) Verify the Stokes' theorem where F = (2x - y)i + (x +z)j + (3x – 2y)k and S is the part of z = 5 – x2 - y2 above the plane z = 1. Assume that S is oriented upwards.
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