Montrer que
1
\(\displaystyle \lim_{n \to \infty} \int_0^n \left(1-\frac{x}{n}\right)^n x^{m}dx = m !\) (pour tout \(m\in \mathbf{N}\)).
2
\(\displaystyle \lim_{n \to \infty} \int_0^n \left(1+\frac{x}{n}\right)^n e^{-2x}dx = 1\).
Montrer que
\(\displaystyle \lim_{n \to \infty} \int_0^n \left(1-\frac{x}{n}\right)^n x^{m}dx = m !\) (pour tout \(m\in \mathbf{N}\)).
\(\displaystyle \lim_{n \to \infty} \int_0^n \left(1+\frac{x}{n}\right)^n e^{-2x}dx = 1\).