6. Evaluate (7xi - zk) · ndA over the sphere S : x² + y² + z² = 4 (u) by the Divergence Theorem, (b) directly.
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- Use the Divergence Theorem to evaluate the flux of F = yi - xj + 2xk across the sphere x ^ 2 + y ^ 2 + z ^ 2 = 25 with outward orientation . Flux of FThe paraboloid z = x2 + y2 - 4x + 2y + 5 has a local minimum at (2, -1). Verify the conclusion of as shown for this function.Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of the region cut from the first octant by the plane y + z = 4 and the elliptical cylinder 4x2 + y2 = 16.
- use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the region cut from the first octant by the plane y+z=4 and the elliptical cylinder 4x^2+y^2=16use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i - 2xyj + 3xzk D: The region cut from the first octant by the sphere x2 + y2 + z2 = 4.Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2 in the xy-plane.
- Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2 <=a2 in the xy-plane.S is the region bounded by paraboloid z=9-x^2-y^2 and the xy planeUse the Divergence Theorem to find the flux of F = xy2i + x2yj + yk outward through the surface of the region enclosed by the cylinder x2 + y2 = 1 and the planes z = 1 and z =-1.