Cos2x 1 2
| Input |
|---|
| cos(2 x)×1×2 |
| Result |
| 2 cos(2 x) |
| Roots |
| x = (pi n)/2 – pi/4, n element Z |
| Series expansion at x=0 |
| 2 – 4 x^2 + (4 x^4)/3 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos(2 x)×2) = -4 sin(2 x) |
| Indefinite integral |
| integral 2 cos(2 x) dx = sin(2 x) + constant |
| Global maxima |
| max{cos(2 x) 2} = 2 at x = pi n for integer n |
| Definite integral |
| integral_0^(pi/4) 2 cos(2 x) dx = 1 |
| Definite integral mean square |
| integral_0^pi (4 cos^2(2 x))/pi dx = 2 |