use divergence theorem Let S be the surface of the box given by {(x, y, z)|...
Let S be the surface of the box given by {(x, y, z)| – 2 < x < 0, -1 <y < 2, 0 Sz<3} with outward orientation. - Let F =< – xln(yz), yln(yz), –22 > be a vector field in R3. Using the Divergence Theorem, compute the flux of F across S. That is, use the Divergence Theorem to compute SSF. ds S
Let S be the surface of the box given by {(x, y, z) – 2 <<<0, -1<y<2, 0<z<3} with outward orientation. Let Ę =< -æln(yz), yln(yz), –22 > be a vector field in R3. Using the Divergence Theorem, compute the flux of F across S. That is, use the Divergence Theorem to compute SS F. ds S
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
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is the sphere (oxy.z): x² + y +z - 6) Use the Divergence Theorem to compute the net outward flux of the field F. (-3x, 2y.72) across the surface S, where The net outward flux across the sphere is (Type an exact answer, using as needed.)
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
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 .
Let S be the surface of the 'liptic paraboloid z = 4 - 22 - y2 above the plane z = 0, and with upward orientation. Let F =< yetan(z), -xcos > be a vector field in R3. 9 + Use Stoke's Theorem to compute: Sf curlĒ. ds. S
10. Use the Divergence Theorem to compute the net outward flux of the vector field F= <x^2, -y^2, z^2> across the boundary of the region D, where D is the region in the first octant between the planes z= 9-x-y and z= 6-x-y. The net outward flux is __. 11. Decide which integral of the Divergence Theorem to use and compute the outward flux of the vector field F= <-7yz,2,-9xy> across the surface S, where S is the boundary of...
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3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
Let F(x, y, z) (xr,y, z). Compute the outward flux of F: 9y2622 on the bounded region inside of S. However, you may wish to consider the region bounded between S and the sphere of radius 100.) 7/Fthrough the ellipsoid 4c2 36. (Hint: Because F is not continuous at zero, you cannot use the divergence theorem Suppose that E is the unit cube in the first octant and F(z,y, z) = (-x,y, z). Let S be the surface obtained by...