2. \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \)

dériver: \( (3-x) e^{x}+1 \)

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

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. \( \lim _{x \rightarrow-\infty}\left(x^{2}-1-\ln \left(1-x^{3}\right)\right) \)

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

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