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1. a) Use the cylindrical coordinates to evaluate (3 + xy)dV, where E is the solid E in the first octant that is bounded by the paraboloid z = 1-x² -y², and the coordinate planes z = 0, x = 0 and y = 0.

1. a) Use the cylindrical coordinates to evaluate (3 + xy)dV, where E is the solid E in the first octant that is bounded by the paraboloid z = 1-x² -y², and the coordinate planes z = 0, x = 0 and y = 0.

Elementary Geometry For College Students, 7e
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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1. a) Use the cylindrical coordinates to evaluate (x³ + xy?)dV, where E is the solid E in the first octant that is bounded by the paraboloid z = 1–x² – y², and the coordinate planes z = 0, x = 0 and y = 0. b) Evaluate 1+ 4x x² + y? + >2dV, E where E is the solid that is inside x2 + y? + z2 = 2z and above both z = 3x2 +3y2 and z = 1.
Transcribed Image Text:1. a) Use the cylindrical coordinates to evaluate (x³ + xy?)dV, where E is the solid E in the first octant that is bounded by the paraboloid z = 1–x² – y², and the coordinate planes z = 0, x = 0 and y = 0. b) Evaluate 1+ 4x x² + y? + >2dV, E where E is the solid that is inside x2 + y? + z2 = 2z and above both z = 3x2 +3y2 and z = 1.
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