4. Start with the region A in the first quadrant enclosed by the x-axis and the parabola y = 2x(2-x). Then obtain solids of revolution S₁, S2, and S3 by revolving A about the lines y = 4, y = (unusual) "doughnuts" which are 8 units across, whose hole is 4 units across, and -2, and x = 4 respectively. All three solids are whose height is 2 units. Sketch them. a) Which do you expect to have larger volume, S₁ or S₂? Compute their volumes exactly and check your guess. b) Compute the volume of S3. (It may be harder to guess in advance how S3 compares in volume to S₂ and S₁.)

4. Start with the region A in the first quadrant enclosed by the x-axis and the parabola y = 2x(2-x). Then obtain solids of revolution S₁, S2, and S3 by revolving A about the lines y = 4, y = (unusual) "doughnuts" which are 8 units across, whose hole is 4 units across, and -2, and x = 4 respectively. All three solids are whose height is 2 units. Sketch them. a) Which do you expect to have larger volume, S₁ or S₂? Compute their volumes exactly and check your guess. b) Compute the volume of S3. (It may be harder to guess in advance how S3 compares in volume to S₂ and S₁.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 8AEXP

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