Find

lim(x,y,z)->(0,0,0) of (xyz)/(x^2+y^2+z^2)

I know it equals zero and I know you can use spherical coordinates but I have not learned that yet and I believe I am supposed to do this with epsilon and delta.

What about :

let epsilon > 0,
choose delta = epsilon :
for every x, y, z such that |x|, |y|, |z| < epsilon, with (x,y,z) not (0,0,0) :
consider m = max ( |x|, |y|, |z| ), notice that 0 < m < epsilon.

On one hand :
|x*y*z| < m^3 (lesser than or equal to)

On other hand :
|x²+y²+z²| > m² (greater than or equal to)

And finally |f(x,y,z)| < m^3 / m² = m < epsilon.

Thank you!!