Solving limit with three variables

[wilcofan3]

Homework Statement

\lim_{(x,y,z) \to (0,0,0)} \frac {x^3 + y^3 + z^3} {x^2 + y^2 + z^2}

Homework Equations

The Attempt at a Solution

I believe the limit is going to 0, but I have yet to find a way to prove this is the case.

 

[Dick]

Let x^2+y^2+z^2=r^2. Then as (x,y,z)->(0,0,0), r->0. But e.g. |x|<r. Do you see what I'm saying?

 

[wilcofan3]

Let x^2+y^2+z^2=r^2. Then as (x,y,z)->(0,0,0), r->0. But e.g. |x|<r. Do you see what I'm saying?

Not quite. I understand what you are doing with the bottom, the equation is that of a sphere, and therefore you are using another equation to show the bottom is going to 0. But how exactly does that prove the numerator is going to 0 as well?

 

[Dick]

If |x|<r and |y|<r and |z|<r, what about |x^3+y^3+z^3|?