ving problems w olume of a rectangu Osoid 9x² + 36y² +

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Solve the following problems with the second partial derivative test and with Lagrange's method.
a) . Find the volume of a rectangular box with sides parallel to the coordinate planes that can be inscribed
in the ellipsoid 9x² + 36y² + 4z² = 36.
b)
. Find the volume of a rectangular box with three sides on the coordinate planes, in the first octant and
a vertex on the plane x + 2y + 3z = 6.
c) . Find the volume of a rectangular box with maximum volume is the surface is 64cm².
Transcribed Image Text:1. Solve the following problems with the second partial derivative test and with Lagrange's method. a) . Find the volume of a rectangular box with sides parallel to the coordinate planes that can be inscribed in the ellipsoid 9x² + 36y² + 4z² = 36. b) . Find the volume of a rectangular box with three sides on the coordinate planes, in the first octant and a vertex on the plane x + 2y + 3z = 6. c) . Find the volume of a rectangular box with maximum volume is the surface is 64cm².
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