(1 point) Verify that the Divergence Theorem is true for the vector field F = 3x´i...
(1 point) Verify that the Divergence Theorem is true for the vector field F-3z2ì + 3z30-22k and the region E the solid bounded by the paraboloid z = 16 z2 y2 and the zy-plane To verify the Divergence Theorem we will compute the expression on each side. First compute div F dV div F div F dV- dz dy dr where div F dV- Now compute F dS Consider S- PU Dwhere P is the paraboloid and D is the...
(1 point) Verify the Divergence Theorem for the vector field and region: F-(2x, 82.9y〉 and the region x2 + y2-1, 0-X 7 (1 point) Verify the Divergence Theorem for the vector field and region: F-(2x, 82.9y〉 and the region x2 + y2-1, 0-X 7
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
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 = 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...
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) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
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 that Stokes' Theorem is true for the vector field Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
. Use the divergence theorem to findZ Z S F · dS where F = hxz2 , exz, y2 zi and S is the surface of the solid bounded by the paraboloid x = 25 − 2y 2 − 2z 2 and the plane x = 7.