Prove that $f(x,y,z)=x^4+y^4+z^4$ is continuous on point $(x,y,z)=(0,0,0)$ with epsilon-delta
I prove this so:
if $$\lim_{x,y,z \to 0,0,0} f(x,y,z) = f(0,0,0)$$ then that function is continuous
$$\lim_{x,y,z \to 0,0,0} x^4+y^4+z^4 = 0^4+0^4+0^4=0$$
But how to prove this with $\epsilon$-$\delta$?