Let F = xi + yj + zk, and let D be the cube bounded by the planes x = y = z = +-1. Let S be the boundary of D. Verify the divergence theorem...
13. Use the divergence theorem to evaluate Sis Fonds where F(x, y, z) - Xi+yj+zk and S is the unit cube in the first octant bounded by the planes x-0, x= 1, y = 0, y - 1,2-0, z - 1. The vector n is the unit outward normal to the cube.
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...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
16.8.5 Use the divergence theorem to find the outward flux of F across the boundary of the region D. D: The cube bounded by the planes x- t2, y- t2, and z- t2 The outward flux is (Type an exact answer.) 16.8.5 Use the divergence theorem to find the outward flux of F across the boundary of the region D. D: The cube bounded by the planes x- t2, y- t2, and z- t2 The outward flux is (Type an...
Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S be any sphere not containing the origin. Find the outward flux of F across S. (c) Let Sa be the sphere of radius a centered at the origin. Find the outward flux of F across Sa.
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently, (x2 + y2 + 22)3/2 f where r = ci + yj + zk and r= |||| = V2 + y2 + z2 (instead of p) 1 F(r) = r2 (a) [10 pts] Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral lle F.NDS where S is the unit sphere x2 + y2 + z2 = 1...
Let F(x, y, z) = xi + yj + zk and S be the surface defined by z = 9 – 22 - y2 and 2 > 0. Evaluate SsFinds, where n is the upward unit normal vector.
Question 3. Let Q be the solid hemisphere bounded by x + y² + 2 = 1 for 2 > 0 and by the plane z = 0, and let F = xi+yi + zk be a vector field. Verify the divergence theorem for Q and F by answering parts (a) and (b) below. Part (a) (5 points). Find the value of the triple integral of the divergence of F over the solid hemisphere Q. Part (b) (10 points). Evaluate...
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=
Please do your best with the handwriting. Thank you very much 14. F(x. y. z)4xzi + yj + 4xyk S: z 9 x2y'. z 20 15. F(x, y. z)i + yj + zk S:z x- y In Exercises 7-18, use the Divergence Theorem to evaluate IJ. F.NdS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results 14. F(x. y. z)4xzi...