[[ (a²z+ y²2) dS, where S is the top half of the sphere S x² + y² + z² = 4. 16 Problem 2. Evaluate ][ (z+x²y) ds, where S is the part of the cylinder S y² + ² = 1 that lies between the planes x = 0 and x = 3 in the first octant. 12 Problem 3. Evaluate ff and xz dS, where S is the part of the plane 2x + 2y +z = 4 that lies in the first octant. 4 Problem 4. Evaluate If x² x²² ds, where S is the part of the cone z² = x² + y² S that lies between the planes z = 1 and 2 = 3. 364√/2π/3 Problem 5. Evaluate If xas x ds, where S is the triangular region with vertices S (1,0,0), (0, -2, 0), and (0,0,4). √21/3 Problem 6. Evaluate ff azd xz dS, where S is the boundary of the region enclosed by the cylinder y² + ² = 9 and the planes x = 0 and x + y = 5. 0 Problem 7. Evaluate !! dS, where S is the paraboloid y = 9-x² - 2² S together with its cap when y = 0. (7/6)[37/37 1] +9T Problem 8. Evaluate. Problem 9. Evaluate. //* F. ds, where F(x, y, z) = xyî + 4x²ĵ + yzk, and S is S the surface with parameterization F(u, v) = ui + vj + ueºk, where 0 ≤ u≤ 2 and 0 ≤v≤1. 16(1-e) •//₁ F. ds, where F(x, y, z) = (x, y, z²) and S is the S part of the unit sphere where x > 0, y > 0, and z < 0. 57/24 Problem 10. Evaluate
[[ (a²z+ y²2) dS, where S is the top half of the sphere S x² + y² + z² = 4. 16 Problem 2. Evaluate ][ (z+x²y) ds, where S is the part of the cylinder S y² + ² = 1 that lies between the planes x = 0 and x = 3 in the first octant. 12 Problem 3. Evaluate ff and xz dS, where S is the part of the plane 2x + 2y +z = 4 that lies in the first octant. 4 Problem 4. Evaluate If x² x²² ds, where S is the part of the cone z² = x² + y² S that lies between the planes z = 1 and 2 = 3. 364√/2π/3 Problem 5. Evaluate If xas x ds, where S is the triangular region with vertices S (1,0,0), (0, -2, 0), and (0,0,4). √21/3 Problem 6. Evaluate ff azd xz dS, where S is the boundary of the region enclosed by the cylinder y² + ² = 9 and the planes x = 0 and x + y = 5. 0 Problem 7. Evaluate !! dS, where S is the paraboloid y = 9-x² - 2² S together with its cap when y = 0. (7/6)[37/37 1] +9T Problem 8. Evaluate. Problem 9. Evaluate. //* F. ds, where F(x, y, z) = xyî + 4x²ĵ + yzk, and S is S the surface with parameterization F(u, v) = ui + vj + ueºk, where 0 ≤ u≤ 2 and 0 ≤v≤1. 16(1-e) •//₁ F. ds, where F(x, y, z) = (x, y, z²) and S is the S part of the unit sphere where x > 0, y > 0, and z < 0. 57/24 Problem 10. Evaluate
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Can please solve problem #10 and show all of your work in pictures do not type it, please! make sure you do the right work, thank you for your help.
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Please solve this problem(#10) again, the answer is supposed to be 5pi/24. Thank you
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