Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.1 Functions of Several Variables - 14.1 Exercises - Page 940: 19


The domain is given by $$\mathcal{D}=\{(x,y)|y\geq x^2,x\neq\pm1\},$$ and it is presented on the graph below (red lines are excluded from it)

Work Step by Step

Here, we have two constraints: 1.The argument of the square root has to be nonnegative i.e. $$y-x^2\geq0\Rightarrow y\geq x^2.$$ 2. The denominator must not be zero i.e. $$1-x^2\neq0\Rightarrow x\neq\pm1.$$ This means that the domain is the region including and above the parabola $y=x^2$ with the vertical lines $x=\pm1$ excluded from is. So we write for the domain $$\mathcal{D}=\{(x,y)|y\geq x^2,x\neq\pm1\},$$ and it is presented in the figure below (red lines are excluded from it)
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