it c 5. Find the surface aren of the part of first octant. e 2y-6 that...
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
Questions Evaluate S 45ydo over the surface S, the first octant of the plane +2y+2z = 4. a) 16 b) 16 3 c) 16 3 d) O-16 8
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 2
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate the flux integral of the vector field F 2i + j + 3k across the surface S (with N being the unit upward vector normal to the plane). B.I 48 C. I 72 E. 1 24 (1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate...
5. (6) Consider the solid bound in the first octant by the surface 9x2 +4y 36 and the plane 9x+ 4y + 6z 36. a. Sketch the solid. b. Set-up the integral to find the volume of the solid by using a double integral. DO NOT INTEGRATE 5. (6) Consider the solid bound in the first octant by the surface 9x2 +4y 36 and the plane 9x+ 4y + 6z 36. a. Sketch the solid. b. Set-up the integral to...
1. Find parametric equations for each surface. a) The plane through the points (0, 0,0), b) The portion of the sphere x2 +y2 + c) The part of the cylinder y 16 (1,0,3), and (0, 2,3) 22-9 inside the first octant, that lies between the planes +4. 1. Find parametric equations for each surface. a) The plane through the points (0, 0,0), b) The portion of the sphere x2 +y2 + c) The part of the cylinder y 16 (1,0,3),...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone 9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S. 13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
Let S be the part of the plane 2x+4y+z=4 2 x + 4 y + z = 4 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F=4i+4j+3k F = 4 i + 4 j + 3 k across the surface S