Chapter 14 - Partial Derivatives - 14.2 Exercises - Page 924: 33

$D=$ {$(x,y) | x^2+y^2 \gt 4$}

As we are given that $G(x,y)=ln(x^2+y^2-4)$ The function $G(x,y)=ln(x^2+y^2-4)$ represents a logrithimic function which is continuous on its domain $D$. Thus, $ x^2+y^2-4 \gt 0$ or, $x^2+y^2 \gt 4$ or, $x^2+y^2 \gt 4$ Hence, Domain: $D=$ {$(x,y) | x^2+y^2 \gt 4$}