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: 26

Answer

This is the half space lying in front of and including the plane $x=-3$.

Work Step by Step

This region is the set of all points $(x,y,z)$ that satisfy the equation $x\geq -3$. So this is the set of all points with $x$-coordinate greater than or equal to -3. We know $x=-3$ is the plane that intersects the $x$-axis at $x=-3$ and is parallel to the $yz$-plane. So since every point in our region has $x$-coordinate greater than or equal to -3, every point must lie in front of the plane $x=-3$. So our region is the half space lying in front of and including the plane $x=-3$.
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