please help me solve the following question 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ F-n dS where F-: (x, y, z) and s is the cone z2 x2 + y2, 0 S 2 1; with the outward pointing normal. 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b. Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
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...
Could you do number 4 please. Thanks 1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of the sphere x2 + y2 + z2-16 in the first octant eBook
Problem 1.20. Let f(z, y)-(X2-y2)/(z2 + y2) 2 for x, y E (0, 1]. Prove that f(x, y) dx dy f f(x,y) dy)dr. Jo Jo JoJo
16. fs y2 dS, S is the part of the sphere x2 + y2 + z2 = 1 that lies above the cone z = Vx2 + y2 16. fs y2 dS, S is the part of the sphere x2 + y2 + z2 = 1 that lies above the cone z = Vx2 + y2
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.
Use Lagrange multipliers to find the min and max of f(x,y,z) = x2-y2+ 2z subject to the constraint x2 + y2 + z2 = 1.
where g is a function of one variable 16. Suppose that f(x,y,z)= g(V x2 + y2 + such that g(3) = 4. Evaluate ſyf(x,y,z)ds' where S is the sphere x² + y2 +z2 =9.