6. find Maclurin expansion of (2 Points) * \( f(x)=e^{x}-1 \) \( f(x)=x-\frac{x^{2}}{2!}-\frac{x^{3}}{3!}-\ldots \) \( f(x)=x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\ldots \) \( f(x)=x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\ldots \). None of these

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}

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

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

\( \left. \begin{array} { l | l | l | l | } { \lim _ { x \rightarrow 3 } ( \frac { x - 3 } { x ^ { 2 } - 9 } ) } \\ { x } & { - 2.99 } & { - 2.999 } & { 3 | 3.001 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. \)

4. For which values of \( x \) will \( \sum_{k=1}^{\infty}(4 x-1)^{k} \) exists.