11.) (19 pts.) Verify the Divergence Theorem for F(q, y, z) = (y)i + (-2) 3...
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.
(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) 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...
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.
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = y z' i + 2yzj + 4z2k across the surface of the solid E enclosed by the paraboloid z = x2 + y2 and the plane z = 9. V
2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cylinder E : r2 + y2 < 4, 0 2. (a) 9 pts] Evaluate F dS directly where S is the closed cylinder S which bounds E oriented outward. Note that S consists of three surfaces: S1 the surface of the cylinder x2 + y-4 for 0 z 2, the disc Di : x2 +92-4 which lies in the plane z 0 and...
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 the Divergence Theorem for F(x, y, z)-(zy, yz, xz) and the solid tetrahedron with vertices (0,0,0), (1,0,0), (0, 2,0), and (0, 0,1 (3) Verify the Divergence Theorem for F(x, y, z)-(zy, yz, xz) and the solid tetrahedron with vertices (0,0,0), (1,0,0), (0, 2,0), and (0, 0,1
. 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.
5. Verify Stokes' theorem for F(x,y, z) = 2zi +3xj + 5yk over the paraboloid z = 4 -x2-y2 z≥06. Verify the divergence theorem for F(x, y,z) = zk over the hemisphere : z = √(a2-x2-y2)