Установите сходимость или расходимость указанных рядов с помощью интегрального признака Коши. \( \begin{array}{lll}\text { 1) } \frac{1}{2 \ln 2}+\frac{1}{3 \ln 3}+\ldots+\frac{1}{(n+1) \ln (n+1)}+\ldots \\ \text { 2) } \frac{1}{2 \ln ^{2} 2}+\frac{1}{3 \ln ^{2} 3}+\ldots+\frac{1}{(n+1) \ln ^{2}(n+1)}+\ldots ; \\ \sum_{n=1}^{\infty} \frac{\ln (n+1)}{(n+1)^{2}} ; & \text { 4) } \sum_{n=2}^{\infty} \frac{1}{\sqrt{n}} \cdot \ln \frac{n+1}{n-1} ; & \text { 5) } \sum_{n=1}^{\infty} \frac{1}{(n+1) \ln (n+1) \ln \ln (n+1)}\end{array} \)

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

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

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

(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

(3) Evaluat \( \frac{\lim }{x-71} \cdot \frac{x^{3}+3 x+4}{2 x^{2}+x-3} \)