. 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.
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Use the Divergence Theorem to calculate the surface integral F · dS; that is, calculate the flux of F across S. F(x, y, z) = (6x3 + y3)i + (y3 + z3)j + 15y2zk, S is the surface of the solid bounded by the paraboloid z = 1 − x2 − y2 and the xy-plane. S
Let F(x,y,z) =( x3z)I+(y3z-yz3)j+z4k use the divergence theorem to calculate ∫∫cF•ds, that is , calculate flux of F across S, where S is the surface of the solid bounded by the hemisphere z = √ 2 - x2 - y2 and the xy - plane .
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π 9. Let Q be the solid bounded by the cylinder x2 + y2...
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F= <2y, y, z2> and S the closed surface formed by the paraboloid z = x2 + y2 and the disk x2 + y2 ≤ 4 at z = 4. Use divergence theorem to solve one way, and use SSs F * N ds to solve the other way. (This is a Calculus 3 problem.) * 36.3. Compute in two ways the fux integral ф...
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
Use the Divergence Theorem to calculate the flux of F across S, where F=zi+yj+zxk and S is the surface of the tetrahedron enclosed by the coordinate planes and the plane x/2+y/5+z=1 ∫∫SF⋅ dS=
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
(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...
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) 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...