Question

Salut, am nevoiecde ajutor la ex. 2.577C

Answer 1

$u- 1< [u] \leq u \\ \\ (nx)-1 < [nx] \leq(nx) \Big|:n\\ \\ x - \dfrac{1}{n}<\dfrac{[nx]}{n}\leq x\\ \\\lim\limits_{n\to \infty}\Big(x-\dfrac{1}{n}\Big)< \lim\limits_{n\to \infty}\dfrac{[nx]}{n}\leq x\\ \\ x < \lim\limits_{n\to \infty}\dfrac{[nx]}{n}\leq x\\ \text{}\quad \searrow\quad\quad\quad\,\,\swarrow \\ \\ \text{}\quad\quad\quad\,\,\,\, x$

$\Rightarrow l = x$

=> b) corect.