University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.1 - Three-Dimensional Coordinate Systems - Exercises - Page 599: 18

Answer

$ a.\quad$ The slab between the planes $x=1$ and $x=0$. $ b.\quad$ The upright square column passing through a unit square in the xy-plane, bordered by planes $x=0,x=1, y=0,y=1.$ $ c.\quad$ A cube with side length 1 in the 1st octant (all coordinates are nonnegative), with the origin as one of its vertices.

Work Step by Step

$a.$ $x=1$ and $x=0$ are parallel planes. $x=0$ is the yz-plane. This compound inequality describes the slab between the planes $x=1$ and $x=0$. $b.$ The part of the slab in part (a) that lies between two parallel planes $y=0$ and $y=1.$ This is an upright square column passing through a unit square in the xy-plane, bordered by planes $x=0,x=1, y=0,y=1.$ $c.$ The part of the square column between the xy-plane $(z=0)$ and $z=1.$ This is a cube with side length 1 in the 1st octant (all coordinates are nonnegative), and one of its vertices is the origin. $ a.\quad$ A slab between the planes $x=1$ and $x=0$ $ b.\quad$ An upright square column passing through a unit square in the xy-plane, bordered by planes $x=0,x=1, y=0,y=1.$ $ c.\quad$ A cube with side length 1 in the 1st octant (all coordinates are nonnegative), with the origin as one of its vertices.
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