\( y ^ { \prime } ( t ) + 2 y + \int _ { 0 } ^ { t } y ( x ) d x \quad y ( 0 ) = 1 \)

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

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

\[ \text { OR } \] Given a function \( f(x)=\left\{\begin{array}{ll}7-4 x, & x<1 \\ x^{2}+2, & x \geq 1\end{array}\right. \) Evaluate \( \operatorname{limit}_{x \rightarrow-6} f(x) \) and \( \operatorname{limit}_{x \rightarrow 1} f(x) \) if exist.

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

If A is differentiable vector function, then \( \nabla \times \nabla \times A \) Select one: \( \nabla \nabla \cdot A-\nabla^{2} A \) 0 \( \nabla^{2} A \) \( \nabla \nabla \cdot A \)