Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, ...
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉 and SS is the top half of the sphere x2+y2+z2=9x2+y2+z2=9. (1 point) Use the Divergence Theorem to evaluate FdS where F2x +3 tan2).^z-1 and S is the top half of the sphere x2 +y2 + z2 -9 Hint: S is not a closed surface. First compute integrals overs, and S2 , where S, is the disk x2 + y2 < 9, z = 0 oriented downward and S2 = S U...
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.
Provide correct answer Use the Divergence Theorem to evaluate //F. ds where F = (4x", 4y?, 17) and S is the sphere x² + y2 + z = 25 oriented by the outward normal. The surface integral equals
(1 point) Let F(x, y, z) = 1z2xi +(x3 + tan(z))j + (1x2z – 5y2)k. Use the Divergence Theorem to evaluate SsF. dS where S is the top half of the sphere x2 + y2 + z2 = 1 oriented upwards. / F. ds = S
(1 point) Verify that the Divergence Theorem is true for the vector field F = 3x´i + 3xyj + 2zk and the region E the solid bounded by the paraboloid z = 9 - x2 - y2 and the xy-plane. To verify the Divergence Theorem we will compute the expression on each side. First compute div F dV JE div F= Waive av = f II Σ dz dy dx where zi = MM y1 = y2 = MM мм...
(1 point) Let F(x, y, z) = 1z- xi + (x2 + tan(z)j + (1x²z + 3y2)k. Use the Divergence Theorem to evaluate /s F. ds where S is the top half of the sphere x2 + y2 + z2 = 1 oriented upwards. SSsF. dS =
Use the Divergence Theorem to evaluate S Ss F.dS where F= = (5x8, 6yz4, -40z?) and S is the boundary of the sphere 22 + y2 + z2 = 9 oriented by the outward normal. The surface integral equals
Use the Divergence Theorem to evaluate \(\iint_{S} \mathbf{F} \cdot d \mathbf{S}\), where \(\mathbf{F}(x, y, z)=z^{2} x \mathbf{i}+\left(\frac{y^{3}}{3}+\cos z\right) \mathbf{j}+\left(x^{2} z+y^{2}\right) \mathbf{k}\) and \(S\) is the top half of the sphere \(x^{2}+y^{2}+z^{2}=4\). (Hint: Note that \(S\) is not a closed surface. First compute integrals over \(S_{1}\) and \(S_{2}\), where \(S_{1}\) is the disk \(x^{2}+y^{2} \leq 4\), oriented downward, and \(S_{2}=S_{1} \cup S\).)
(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...
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) -...