Xosmas integrallarni hisoblang yoki uzoqlashuvchi ekanini aniqlang \[ \int_{e^{2}}^{\infty} \frac{d x}{x \ln \ln x} \]

6. \( \lim _{x \rightarrow 2}\left(\frac{x^{2}-5 x+6}{x-2}\right) \) \begin{tabular}{l|l|l|l|l|}\( x \) & 1.99 & 1.999 & 2 & 2.001 \\ \hline\( f(x) \) & & & & \\ \hline\end{tabular}

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | } \hline & { - 0.001 } & { 0 } \\ { F ( x ) } & { 0.001 } \\ \hline \end{array} \right. } \end{array} \right. \)

(3) Derive the formula for the volume of a Cylinder by using integration? (3 mark)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l | } { x } & { - 0.001 } & { 0 } & { 0.001 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

(1)- \( \int_{-\infty}^{\infty} \frac{e^{x}}{1+e^{2 x}} \mathrm{dx} ? \)