Chapter 13.2, Problem 77E

Finding a Limit Using Spherical Coordinates In Exercises 77 and 78, use spherical coordinates to find the limit.[ Hint: Let $x=\rho \sin \varphi \cos \theta ,y=\rho \sin \varphi \sin \theta$. and, $z=\rho \cos \varphi$, and note that $(x,y,z)\to (0,0,0)$ implies $\rho \to 0^{\circ }$.]

$\underset{(x,y)\to (0,0,0)}{\lim }\frac{xyz}{x^2+y^2+z^2}$