Cube root of x^2
| Input |
|---|
| cuberoot(x^2) |
| Result |
| (x^2)^(1/3) |
| Alternate form assuming x>0 |
| x^(2/3) |
| Root |
| x = 0 |
| Series expansion at x=0 |
| (x^2)^(1/3) + O(x^62194) (Puiseux series) |
| Series expansion at x=∞ |
| x^(2/3) + O((1/x)^(186580/3)) (Puiseux series) |
| Derivative |
| d/dx(cuberoot(x^2)) = (2 x)/(3 (x^2)^(1/3)^2) |
| Indefinite integral |
| integral cuberoot(x^2) dx = 3/5 x (x^2)^(1/3) + constant |
| Global minimum |
| min{cuberoot(x^2)} = 0 at x = 0 |
| Series representation |
| (x^2)^(1/3) = sum_(n=0)^infinity (script c)_n (-1 + x)^n for ((script c)_0 = 1 and (-2 + 3 n) (script c)_n + (3 + 3 n) (script c)_(1 + n) = 0) |