Исследовать на сходимость ряды с положительными членами \( \sum_{n=1}^{\infty} \frac{(n+2)!}{n^{n}} \). \( \sum_{n=1}^{\infty} \frac{n+3}{n(n+1)} \)

1. \( \lim _{x \rightarrow 2} \frac{x-2}{x^{2}-x-2} \) \begin{tabular}{l|l|l|l|l|l|}\( x \) & 1.9 & 1.99 & 1.999 & 2 & 2.001 \\ \hline\( f(x) \) & 2.01 & 2.1 \\ \hline\end{tabular}

(iv) In integral equation of the form \( \int_{0}^{1} \frac{F(u) d u}{(t-u)^{n}}=G(t) \) is called. (a) Exact equation (b) Convolution type (c) Integro-differential equation (d) Abel's equation

кцияның туындысын табыңыз: \( \left\{\begin{array}{l}x=t^{3}+3 t^{2}-5 \\ y=3 t^{2}+6 t-3\end{array}\right. \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 2 } \frac { x - 2 } { x ^ { 2 } - x - 2 } } \\ { \left. \begin{array} { l | l | l | l | l | l | l | l | } { } \\ { x } & { 1.9 } & { 1.99 } & { 1.999 } & { 2 } & { 2.001 } & { 2.01 } & { 21 } \\ \hline f ( x ) & { } & { } & { } & { } & { } \end{array} \right. } \end{array} \right. \)

Find the equation of trangent to the carve \( g=2 x^{2}+3 x+5 \) at \( x=0 \)