\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } \frac { \sqrt { x + 3 } - \sqrt { 3 } } { x } } \\ { x } \\ \hline x ( x ) \\ \hline f | \end{array} \right. \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 3 } ( \frac { x - 3 } { x ^ { 2 } - 9 } ) } \\ \hline x ( x ) \\ \hline - 2.99 \\ \hline \end{array} \right. \)

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

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

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

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