Bonjour,
quand x → +∞ :
√(x² + 1) - 2x
= 2x[√(x² + 1)/2x- 1]
= 2x[√(x² + 1)/√(4x²) - 1]
= 2x[√[(x² + 1)/4x²]- 1]
= 2x[√(1/4 + 1/4x²) - 1]
En +∞, 1/4x² → 0
donc lim (...) = lim 2x[√(1/4) - 1) = lim 2x(1/2 - 1) = lim (-x) = -∞
