40. Let \( f(x)=x^{3}-12 x+1 \) be defined on \( [0,3] \). What is the range of \( f \) ? \( \begin{array}{llll}\text { A. }(-\infty, \infty) & \text { B. }(-\infty, 1] & \text { C. }[-15,1] & \text { D. }[-15,17]\end{array} \)

Definimos \( G \) como \( G(x)=2 g(x)-h(x)+8 \) \( G^{\prime}(3)= \)

\( \int \operatorname { arctg } \sqrt { 6 x - 1 } d x . \)

Kasr ratsional funksiyalarning integrallarini hisoblang. \[ \int \frac{x+2}{\left(x^{2}-2 x+3\right)^{2}} d x \]

41) \( \lim _{x \rightarrow \pi}\left(x^{2}-\pi^{2}\right) \tan \frac{x}{2} \)

Nyuton usulidan foydalanib, tenglamaning ildizini sakkiz xonali kasrgacha to'g'ri hisoblang. Dastlabki taxminlarni topish uchun grafik chizishdan boshlang. f \( f(x)=-x^{3}+4 x^{2}-2 x-14 \rightarrow \min , \varepsilon=0.001 \) xatolik bilan Nyuton usulida optimizatsiya masalasi yechimi topilsin.