Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 3

Answer

Domain: x and y can be any real numbers except 0, that is $x\ne0, y\ne0$ Range: $g(x,y) \ne 0$ Level curves: $\frac{1}{xy} = c$ (constant).

Work Step by Step

Function: $g(x,y) = \frac{1}{xy}$ Domain: x and y can be any real numbers except 0, that is $x\ne0, y\ne0$ Range: $g(x,y) \ne 0$ Level curves: $g(x,y) = c$ (constant). $\frac{1}{xy} = c$ $xy = \frac{1}{c}$ For example, when $c = 1$, the level curve $xy = 1$ is shown in the figure.
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