Multivariable Calculus, 7th Edition

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

Chapter 12 - Vectors and the Geometry of Space - 12.1 Exercises - Page 815: 27

Answer

This is the slab of space between and including the planes $z=0$ and $z=6$.

Work Step by Step

This region is the set of all points $(x,y,z)$ that satisfy the equation $0 \leq z \leq 6$. We know $z=0$ is the $xy$-plane, and $z=6$ is the plane that intersects the $z$-axis at the point $(0,0,6)$ and is parallel to the $xy$-plane. So since every point in our region has $z$-coordinate with $0\leq z \leq 6$, every point must lie in or between the planes $z=0$ and $z=6$. Hence, our region is the slab of space between and including the planes $z=0$ and $z=6$.
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