## Calculus 8th Edition

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