Hii !

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

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

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

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

E(x) : The Floor of x .