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: 4

Answer

Domain: x and y are real numbers which satisfy: $x^{2}-y \geq 0$ Range: $g(x,y) \geq 0$ Level curves: $y=x^{2}+c^{2}$ which are a series of parabolas

Work Step by Step

Function: $g(x,y) = \sqrt {x^{2}-y}$ Domain: x and y are real numbers which satisfy: $x^{2}-y \geq 0$ Range: $g(x,y) \geq 0$ Level curves: $g(x,y)=c$ (constant) $\sqrt {x^{2}-y}=c$ $y=x^{2}+c^{2}$ which are a series of parabolas For example, when $c=1$, $y=x^{2}+1$ is shown in the figure.
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