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: 25

Answer

This is the half space that lies to the left of the plane $y=8$.

Work Step by Step

This region is the set of all points $(x,y,z)$ that satisfy the equation $y\lt 8$. So this is the set of all points with $y$-coordinate less than 8. We know $y=8$ is the plane that intersects the $y$-axis at $y=8$ and is parallel to the $xz$-plane. So since every point in our region has $y$-coordinate less than 8, every point must lie to the left of the plane $y=8$. So our region is the half space that lies to the left of the plane $y=8$.
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