The discussion revolves around evaluating the limit of a function involving three variables as they approach zero. The specific limit in question is \(\lim_{(x,y,z) \to (0,0,0)} \frac {x^3 + y^3 + z^3} {x^2 + y^2 + z^2}\), which falls under the subject area of multivariable calculus.
The discussion is ongoing, with participants examining different aspects of the limit. Some guidance has been offered regarding the relationship between the numerator and denominator, but there is no explicit consensus on the limit's value yet.
Participants are considering the implications of the variables approaching zero and the relationships between their magnitudes. There is an emphasis on understanding the behavior of both the numerator and denominator in the limit expression.
Dick said: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?