lim (1 + x)1/x = e
x → 0
lim (1 + y/x)x = ey
x → ∞
lim (xn - cn) / (x - c) = nˇ cn-1
x → c
lim (ax - 1) / x = ln a (a > 0)
x → 0
| lim 1 / (1 + ax) = x → ∞ |
1 si a < 1 1/2 si a = 1 0 si a > 1 |
lim xn / ax = 0 (a > 1 ; n Є
N)
x → ∞
lim an / n! = 0 (n Є N)
x → ∞
| lim (sin x) / x = 1 x en radians x → 0 |
| lim (sin z) / z = π / 180 z en degrés z → 0 |
Pour x en radians :
| lim (sin nx) / x = n x → 0 |
lim (tan x) / x = 1 x → 0 |
|
| lim (sin nx) / (sin mx) = n / m x → 0 |
lim (tan nx) / x = n x → 0 |
|
| lim (sin x) / x = 0 x → ∞ |
lim (tan nx) / (tan mx) = n / m x → 0 |
|
| lim arctan 1/x = π
/ 2 x → 0+ |
lim arctan 1/x = -π
/ 2 x → 0- |
