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TP-4 Find the volume of the solid that lies below the paraboloid z = 4 - x² - y², above the xx-plane, and inside the cylinder (x − 1)² + y² = 1. Take note that the solid S under consideration lies above the disk R bounded by the circle with center (1, 0) and radius 1. This unit circle has polar equation r = 2cos, as can be verified by replacing x and y in the rectangular equation of the circle x = r cose and y = r sine. Therefore, R = {(r, 0) | -π/2 ≤ 0 ≤ π/2, 0 < r ≤ 2 cos} and may be viewed as being r-simple, where gi(0) = 0 and g2(0) = 2 cose. Hint: Use the relationship x² + y² = r² and take advantage of symmetry.

TP-4 Find the volume of the solid that lies below the paraboloid z = 4 - x² - y², above the xx-plane, and inside the cylinder (x − 1)² + y² = 1. Take note that the solid S under consideration lies above the disk R bounded by the circle with center (1, 0) and radius 1. This unit circle has polar equation r = 2cos, as can be verified by replacing x and y in the rectangular equation of the circle x = r cose and y = r sine. Therefore, R = {(r, 0) | -π/2 ≤ 0 ≤ π/2, 0 < r ≤ 2 cos} and may be viewed as being r-simple, where gi(0) = 0 and g2(0) = 2 cose. Hint: Use the relationship x² + y² = r² and take advantage of symmetry.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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TP-4 Find the volume of the solid that lies below the paraboloid z = 4 - x² - y², above the xx-plane, and inside the cylinder (x - 1)² + y² = 1. Take note that the solid S under consideration lies above the disk R bounded by the circle with center (1, 0) and radius 1. This unit circle has polar equation r = 2cose, as can be verified by replacing x and y in the rectangular equation of the circle x = r cose and y = r sine. Therefore, R = {(r, 0) | -π/2 ≤ 0 ≤ π/2, 0 < r ≤ 2 cos} and may be viewed as being r-simple, where gi(0) = 0 and g2(0) = 2 cose, Hint: Use the relationship x² + y² = r² and take advantage of symmetry.
Transcribed Image Text:TP-4 Find the volume of the solid that lies below the paraboloid z = 4 - x² - y², above the xx-plane, and inside the cylinder (x - 1)² + y² = 1. Take note that the solid S under consideration lies above the disk R bounded by the circle with center (1, 0) and radius 1. This unit circle has polar equation r = 2cose, as can be verified by replacing x and y in the rectangular equation of the circle x = r cose and y = r sine. Therefore, R = {(r, 0) | -π/2 ≤ 0 ≤ π/2, 0 < r ≤ 2 cos} and may be viewed as being r-simple, where gi(0) = 0 and g2(0) = 2 cose, Hint: Use the relationship x² + y² = r² and take advantage of symmetry.
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