Multivariable limit which should be simple ! How to calculate the following limit WITHOUT using spherical coordinates? 
$$
\lim _{(x,y,z)\to (0,0,0) } \frac{x^3+y^3+z^3}{x^2+y^2+z^2} 
$$
?
Thanks in advance

Let $\epsilon \gt 0$. If $(x,y,z)$ is close enough to $(0,0,0)$ but not equal to it, then $|x^3|\le \epsilon x^2$, with similar inequalities for $|y^3|$ and $|z^3|$. It follows that
$$\frac{|x^3+y^3+z^3|}{x^2+y^2+z^2}\le \frac{|x^3|+|y^3|+|z^3|}{x^2+y^2+z^2}\le \frac{\epsilon (x^2+y^2+z^2)}{x^2+y^2+z^2}.$$ 
