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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 9 - y² 36 + 25 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: =

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9 - y² 36 + 25 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: =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please answer both problems, thank u soso much!

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid + + 9 36 25 G = 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 + + 9 36 25 G = 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:
Find the absolute maximum and minimum of the function f(x, y) = y√x – y² − x + 3y on the domain 0 ≤ x ≤ 9,0 ≤ y ≤ 1. Absolute minimum value: Absolute maximum value: attained at attained at In each case, your second answer should be one or more points (x, y). If there is more than one point at which the maximum or minimum value is attained, enter them all separated by commas (e.g. (1,2),(1,3)).
Transcribed Image Text:Find the absolute maximum and minimum of the function f(x, y) = y√x – y² − x + 3y on the domain 0 ≤ x ≤ 9,0 ≤ y ≤ 1. Absolute minimum value: Absolute maximum value: attained at attained at In each case, your second answer should be one or more points (x, y). If there is more than one point at which the maximum or minimum value is attained, enter them all separated by commas (e.g. (1,2),(1,3)).
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