Question

a) ) lim n infty (2n+1)(n-3) (n+2)(n+4)

Answer 1

$\lim_{n \to \infty} \frac{(2n + 1)(n - 3)}{(n + 2)(n + 4)} = \lim_{n \to \infty} \frac{2 {n}^{2} - 6n + n - 3 }{ {n}^{2} + 4n + 2n + 8} = \lim_{n \to \infty} \frac{2 {n}^{2} - 5n - 3 }{ {n}^{2} + 6n + 8} = \lim_{n \to \infty} \frac{ {n}^{2} (2 - \frac{5}{n} - \frac{3}{ {n}^{2} } ) }{ {n}^{2}(1 + \frac{6}{n} + \frac{8}{ {n}^{2} }) } = \frac{2}{1} = 2$

Ответ: 2