Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Section 14.1 - Functions of Several Variables - Exercises 14.1 - Page 787: 7

Answer

$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x\neq y$ and $y\neq x^{3}$ $\}$
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Work Step by Step

f is defined for points (x,y) that do not yield zero in the denominator. We exclude all points for which $\left\{\begin{array}{l} y=x\\ y=x^{3} \end{array}\right.$ We graph the line and the cubic curve with dashed lines. Domain: all points not lying on either of the graphs of $\left\{\begin{array}{l} y=x\\ y=x^{3} \end{array}\right.$. or, in set notation, $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x\neq y$ and $y\neq x^{3}$ $\}$
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