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 $X=x^3$, $Y=y^4$, $Z=z^{5}$. Then $r^2=X^2+Y^2+Z^2=x^6+y^8+z^{10}$ and
$$|x^3y^3z^2|=|X||Y|^{3/4}|Z|^{2/5}\leq r^{1+3/4+2/5}=r^{43/20}$$
where
$$X=r\cos\theta\cos\phi,\quad Y=r\cos\theta\sin\phi,\quad Z=r\sin\theta\ .$$
Therefore, as $(x,y,z)\to(0,0,0)$, it follows that $r\to 0$ and
$$\left|{x^3y^3z^2\over x^6+y^8+z^{10}}\right|\leq {r^{43/20}\over r^2}=r^{3\over 20}\to 0.$$
