\( \frac { d } { d x } ( \frac { 1 } { ( a x + b ) ^ { m } } ) \)

\( \int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { \sin x } { 1 + \tan x } d x \)

dériver: \( (3-x) e^{x}+1 \)

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

Let \( f \) be a strictly monotonic differen- tiable function on the closed interval \( [5,10] \) such that \( f(5)=6 \) and \( f(10)= \) 26. Which of the following must be true for the function \( f \) on the interval [5,10]? I. The average rate of change of \( f \) is 4. II. The absolute maximum value of \( f \) is 26 . III. \( f(8)>0 \). (A) I only (B) II only (C) III only (D) I and II (E) I. II. and III

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.