Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Multiple Integrals - 15.2 Exercises - Page 1011: 23

Answer

The solid is a part of the 1st octant between the square in the plane $z=0$ and $z=4-x-2y.$

Work Step by Step

The graph of $f(x, y)=4-x-2y $ is a plane, $0\leq x\leq 1$ and $0\leq y\leq 1,$ and $z=f(x,y)$ is least when $x=1, y=1$, so the solid is the first octant. The solid is part of the 1st octant between the planes $z$=0 and $z=4-x-2y.$
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