Chapter 13 - Partial Derivatives - 13.1 Functions Of Two Or More Variables - Exercises Set 13.1 - Page 915: 23

Domain of $f(x, y) \epsilon(-1,1)$

We have to find and plot the domain of $f(x, y)$ We know that the function $\ln x$ has the domain $x>0$. So here, it should be: \[ \begin{array}{l} 1-x^{2}-y^{2}>0 \\ \Rightarrow x^{2}+y^{2}<1 \end{array} \] The plot is below.