Sqrt(4-x^2)
| Input |
|---|
| sqrt(4 – x^2) |
| Alternate form |
| sqrt(2 – x) sqrt(x + 2) |
| Series expansion at x=-2 |
| 2 sqrt(x + 2) – 1/4 (x + 2)^(3/2) – 1/64 (x + 2)^(5/2) + O((x + 2)^(7/2)) (Puiseux series) |
| Series expansion at x=0 |
| 2 – x^2/4 – x^4/64 + O(x^5) (Taylor series) |
| Series expansion at x=2 |
| 2 sqrt(2 – x) + 1/4 sqrt(2 – x) (x – 2) – 1/64 sqrt(2 – x) (x – 2)^2 + 1/512 sqrt(2 – x) (x – 2)^3 – (5 sqrt(2 – x) (x – 2)^4)/16384 + O((x – 2)^5) (generalized Puiseux series) |
| Series expansion at x=∞ |
| sqrt(-x^2) – (2 sqrt(-x^2))/x^2 + O((1/x)^4) (Puiseux series) |
| Derivative |
| d/dx(sqrt(4 – x^2)) = -x/sqrt(4 – x^2) |
| Indefinite integral |
| integral sqrt(4 – x^2) dx = 1/2 sqrt(4 – x^2) x + 2 sin^(-1)(x/2) + constant |
| Global maximum |
| max{sqrt(4 – x^2)} = 2 at x = 0 |