Cosx 3
| Input |
|---|
| cos(x)×3 |
| Result |
| 3 cos(x) |
| Alternate form |
| (3 e^(-i x))/2 + (3 e^(i x))/2 |
| Roots |
| x = pi n – pi/2, n element Z |
| Series expansion at x=0 |
| 3 – (3 x^2)/2 + x^4/8 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos(x)×3) = -3 sin(x) |
| Indefinite integral |
| integral 3 cos(x) dx = 3 sin(x) + constant |
| Global maxima |
| max{cos(x) 3} = 3 at x = 2 pi n for integer n |
| Definite integral |
| integral_0^(pi/2) 3 cos(x) dx = 3 |
| Definite integral mean square |
| integral_0^(2 pi) (9 cos^2(x))/(2 pi) dx = 9/2 = 4.5 |