limit of a function of three variables I would like to ask you how to solve the limit at the origin of the following function: 
$$f(x,y,z)=\frac{x^3y^3z^2}{x^6+y^8+z^{10}}$$
I am quite sure that it is $0$, but I cannot find a function majorizing $f$ and going to $0$ at the origin (in order to use the sandwich thm).
Thank you in advance for your help.
P.S.:I am looking for an alternative method than using spherical coordinates.

Let $x'=x^3$, $y'=y^4$ and $z'=z^5$.  Then, we have
$$\lim_{(x,y,z)\to (0,0,0)}\frac{x^3y^3z^2}{x^6+y^8+z^5}=\lim_{(x',y',z')\to (0,0,0)}\frac{x'y'^{3/4}z'^{2/5}}{x'^2+y'^2+z'^2}$$
Conversion to spherical coordinates $(r,\theta,\phi)$ where $x'=r\sin(\theta)\cos(\phi)$, $y'=r\sin(\theta)\sin(\phi)$, and $z'=r\cos(\theta)$ reveals that
$$\lim_{(x',y',z')\to (0,0,0)}\frac{x'y'^{3/4}z'^{2/5}}{x'^2+y'^2+z'^2}=\lim_{r\to 0}\frac{r^{43/40}\sin^{7/4}(\theta)\cos^{2/5}(\theta)\cos(\phi)\sin^{4/3}(\phi)}{r^2}$$ 
which clearly approaches zero!
