Integrate \( f(x)=\frac{1}{\left(x^{2}+4\right)\left(x^{2}+2\right)} \) use partia fraction

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

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

O64ncirib \( \frac{1}{\pi^{1}} \int_{-7}^{0} \sqrt{49-x^{2}} d x \) Використовуючи рівняння кола \[ x^{2}+y^{2}=49 \]

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.

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.