1. Let a, b and c be 1, 1 and 9 respectively Consider the ellipsoid & given by the equations + = 1. a² 62 c² (a) Let P₁ = (±x, ±y, ±z) be the vertices of a rectangle inscribed in E. Explain why the volume of & is given by V = 8xyz. (b) Use the method of Lagrange multipliers to determine the largest possible volume of E.
1. Let a, b and c be 1, 1 and 9 respectively Consider the ellipsoid & given by the equations + = 1. a² 62 c² (a) Let P₁ = (±x, ±y, ±z) be the vertices of a rectangle inscribed in E. Explain why the volume of & is given by V = 8xyz. (b) Use the method of Lagrange multipliers to determine the largest possible volume of E.
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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Transcribed Image Text:1. Let A, b and c be
1, 1 and 9 respectively
y²
Consider the ellipsoid & given by the equations
2²=1.
a²
6²
(a) Let P; = (±x, ±y, ±z) be the vertices of a rectangle inscribed in Ɛ. Explain
why the volume of & is given by V = 8xyz.
+
(b) Use the method of Lagrange multipliers to determine the largest possible
volume of E.
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could you also do part b for this and on a piece of paper preferably.
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could please write this in on a piece of paper, so that it is easier to understand?
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