Hii !

1) prove That : $\displaystyle \forall x \in \mathbb{R}^*$ , $\displaystyle \vert x . \sin (\frac{1}{x^2}) \vert \leq \vert x \vert $

- Calculat : $\displaystyle \lim_{x \rightarrow 0} x . \sin (\frac{1}{x^2})$ .

2) prove That : $\displaystyle \forall x \in \mathbb{R}^*$ , $\displaystyle 3x-2x^2 < x^2(E(\frac{1}{x}) + E(\frac{2}{x}) ) \leq 3x$

- Calculat : $\displaystyle \lim_{x \rightarrow 0} x^2 ( E(\frac{1}{x}) + E(\frac{2}{x}) )$

$\displaystyle E(x)$ : The Floor of x .