Chapter 13.2, Problem 27ES

Evaluate the limits by converting to spherical coordinates $\left(\rho ,\theta ,\varphi \right)$ and by observing that $\rho \to 0^{+}$ if and only if $\left(x,y,z\right)\to \left(0,0,0\right).$

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