Test 3

$\boxed{1.}\underset{x\to x_0}{\lim }\left(\mathrm{(f}+\mathrm{g)}\right)\left(\mathrm{(x)}\right)=\mathcal{l}+\mathcal{l}‘$ $\boxed{2.}\underset{x\to x_0}{\lim }\left(\mathrm{(f}.\mathrm{g)}\right)\left(\mathrm{(x)}\right)=\mathcal{l}.\mathcal{l}‘$ $\boxed{3.}\mathcal{l}‘\ne 0\Rightarrow \underset{x\to x_0}{\lim }\left(\frac{1}{g}\right)\left(\mathrm{(x)}\right)=\frac{1}{\mathcal{l}‘}et\underset{x\to x_0}{\lim }\left(\frac{f}{g}\right)\left(\mathrm{(x)}\right)=\frac{\mathcal{l}}{\mathcal{l}‘}$ $\boxed{\mathrm{A.}}\underset{x\to x_0}{\lim }(f+g)(x)=\mathrm{l}+{\mathrm{l}}^{\mathrm{\prime }}$ $\boxed{\mathrm{B.}}\underset{x\to x_0}{\lim }(f.g)(x)=\mathrm{l.l}\mathrm{\prime }$ $\mathrm{C.}{\mathrm{l}}^{\mathrm{\prime }}\ne 0\Rightarrow \underset{x\to x_0}{\lim }\left(\frac{1}{g}\right)(x)=\frac{\mathrm{l}}{{\mathrm{l}}^{\mathrm{\prime }}}$ $3.{\mathrm{l}}^{\mathrm{\prime }}\ne 0\Rightarrow \underset{x\to x_0}{\lim }\left(\frac{1}{g}\right)(x)=\frac{\mathrm{l}}{{\mathrm{l}}^{\mathrm{\prime }}}$ et $\underset{x\to x_0}{\lim }\left(\frac{f}{g}\right)(x)=\frac{\mathrm{l}}{{\mathrm{l}}^{\mathrm{\prime }}}$ $$E_{pp}=mgy+cte\text{avec}{E}_{pp}=0$$ $\text{Au point de coordonnee}z=0$ $:E_{pp}=mg.y;E_{pe}=\frac{1}{2}k{y}^2$ fin