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ind the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid y² ₂2 + + = 1 25 1 81 int: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and assume your volume h ne form V = 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which li the first octant. Maximum volume:

ind the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid y² ₂2 + + = 1 25 1 81 int: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and assume your volume h ne form V = 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which li the first octant. Maximum volume:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x² y² 2² 25 + 1 81 1 Hint: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and assume your volume has the form V 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: =
Transcribed Image Text:Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x² y² 2² 25 + 1 81 1 Hint: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and assume your volume has the form V 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: =
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