Exp 2x
| Input |
|---|
| exp(2 x) |
| Exact result |
| e^(2 x) |
| Roots |
| (no roots exist) |
| Periodicity |
| periodic in x with period i pi |
| Series expansion at x=0 |
| 1 + 2 x + 2 x^2 + (4 x^3)/3 + (2 x^4)/3 + O(x^5) (Taylor series) |
| Derivative |
| d/dx(exp(2 x)) = 2 e^(2 x) |
| Indefinite integral |
| integral e^(2 x) dx = e^(2 x)/2 + constant |
| Limit |
| lim_(x->-infinity) e^(2 x) = 0 |
| Definite integral |
| integral_(-infinity)^0 e^(2 x) dx = 1/2 = 0.5 |
| Definite integral over a half-period |
| integral_0^((i pi)/2) e^(2 x) dx = -1 |