Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises - Page 951: 36


$f(x,y,z)$ is continuous for value $y \geq x^2$ and $z \gt 0$

Work Step by Step

As we are given that $f(x,y,z)=\sqrt {y-x^2} \ln z$ The function $f(x,y,z)=\sqrt {y-x^2} \ln z$ represents a represents a squared root function which cannot be less than $0$. Thus, $ \sqrt {y-x^2} \geq 0$ or, $y \geq x^2 $ and $\ln z \gt 0$ or $z \gt 0$ This means that $ y \geq x^2 ; z \gt 0$ Hence, $f(x,y,z)$ is continuous for value $y \geq x^2$ and $z \gt 0$
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