solve using direct method then prove using Stokes’ theoremHomework Answers
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3 Verify Stok sa theorem, for v = ys_ yz,3r+ 2x2, x3 +v) and C's the curve of intersection of the...
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk....
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk. Use Stokes' theorem to calculate S/CD x A) . nds where S is the surface of the cone z = 2 - V x2 + y2 above the zy plane. You may use the formula n cos" u du = – cos”- u sin u + 2 -1 [ cos”-2 u du.
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...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S h...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
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...
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y²...
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y² k, where S is the surface of the paraboloid 2 = 4 – 22 - y2 and C is the curve of intersection of the paraboloid with the plane z = 0.
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...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 inter...
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 intersec ts the plane z y in a curve C. Calculate the circulation 10. The paraboloid z of v 2zi+ x j + y k around C by using Stokes Theorem.
9. The upper half of the ellipsoid tr + ty?...
4. Verify Stokes' Theorem for v = (y – 2 + 2)i + (yz + 4)j...
4. Verify Stokes' Theorem for v = (y – 2 + 2)i + (yz + 4)j – xzk where S is the surface of the cube bounded by x = 0, y = 0, z = 0, x = 2, y = 2, z = 2 with the face in the (x, y) - plane (i.e. z = 0) missing.
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.
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk. Use Stokes' theorem to calculate S/CD x A) . nds where S is the surface of the cone z = 2 - V x2 + y2 above the zy plane. You may use the formula n cos" u du = – cos”- u sin u + 2 -1 [ cos”-2 u du.
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...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
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...
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y² k, where S is the surface of the paraboloid 2 = 4 – 22 - y2 and C is the curve of intersection of the paraboloid with the plane z = 0.
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...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 intersec ts the plane z y in a curve C. Calculate the circulation 10. The paraboloid z of v 2zi+ x j + y k around C by using Stokes Theorem.
9. The upper half of the ellipsoid tr + ty?...
4. Verify Stokes' Theorem for v = (y – 2 + 2)i + (yz + 4)j – xzk where S is the surface of the cube bounded by x = 0, y = 0, z = 0, x = 2, y = 2, z = 2 with the face in the (x, y) - plane (i.e. z = 0) missing.
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.
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