2) \( f(x)=5+2 x-x^{2} \) จาก \( x=-1 \) ถึง \( x=1 \)

X Exercice 28: Calculer les limites suivantes: \( \begin{array}{ll}\text { 1. } \lim _{x \rightarrow-\infty} \ln \left(\frac{x^{2}+x+1}{3+2 x^{2}}\right) & \text { 2. } \lim _{x \rightarrow+\infty}\left(\frac{x^{3}-2}{x}\right) \\ \text { 3. } \lim _{\substack{x \rightarrow 2 \\ x<2}} \ln \left(\frac{x+1}{-x+2}\right) & \text { 4. } \lim _{\substack{x \rightarrow 0 \\ x>0}} \ln \left(\frac{\sin x}{x^{2}+1}\right)\end{array} \)

Exercice 27: Calculer les limites suivantes : \( \begin{array}{ll}\text { 1. } \lim _{x \rightarrow 2} \ln (2-x) & \text { 2. } \lim _{x \rightarrow 1^{+}}\left(x^{2}-1\right) \ln (x-1) \\ \text { 3. } \lim _{x \rightarrow 0^{+}}\left(x^{3}-x\right) \ln x & \text { 4. } \lim _{x \rightarrow-1^{+}}\left(\frac{1}{x+1}+\ln (1+x)\right)\end{array} \)

Prove that the sequence \( \left\langle\mathrm{S}_{n}\right\rangle \) where: \[ s_{n}=\frac{1}{1!}+\frac{1}{2!}+\ldots \ldots+\frac{1}{n!} \] is convergent.

d. \( \int x^{-\frac{4}{3}} d x= \)

Exercice 47 : Calculer les limites suivantes: \( \lim _{x \rightarrow+\infty} x(\ln (x+1)-\ln x) \) 2. \( \lim _{x \rightarrow+\infty}\left(x+\frac{\ln \left(x^{2}-x+2\right)}{x-1}\right) \) 3. \( \lim _{x \rightarrow-\infty}\left(x^{2}-1-\ln \left(1-x^{3}\right)\right) \)