Q: limit of f(x,y)=(x^3-y^3)/(x^2+y^2) as (x,y) -> (0,)?
What I tried:
1. Picked 0 as L
2. We know x^2+y^2 < d^2
3. and lxl=<d and lyl=<d
I can't think of an inequation needed
Any help would be greatly appreciated. Thanks
Q: limit of f(x,y)=(x^3-y^3)/(x^2+y^2) as (x,y) -> (0,)?
What I tried:
1. Picked 0 as L
2. We know x^2+y^2 < d^2
3. and lxl=<d and lyl=<d
I can't think of an inequation needed
Any help would be greatly appreciated. Thanks
If
$\displaystyle
\left(x^2+y^2\right)^{3/2} \le x^3 - y^3 \le \left(x^2+y^2\right)^{3/2},$
then
$\displaystyle
\left(x^2+y^2\right)^{1/2} \le \frac{x^3 - y^3}{x^2+y^2} \le \left(x^2+y^2\right)^{1/2},$
then
$\displaystyle
\left|\, \frac{x^3 - y^3}{x^2+y^2} \, \right| \le \left(x^2+y^2\right)^{1/2}.$