问题

Questions in category: 极限 (Limit).

极限证明题

Posted by haifeng on 2014-11-28 19:18:52 last update 2023-08-23 09:11:26 | Answers (1) | 收藏

设 $f \in C^{2} [0, 1]$ , 满足 $f (1) = 0$ , $f^{'} (1) = a$ . 证明

$lim_{n \to \infty} n^{2} \int_{0}^{1} x^{n} f (x) d x = - a .$