7. Let \( S \) be an open surface which is the portion of the paraboloid \( z=16-x^{2}-y^{2} \) lying above the plane \( z=7 \). Evaluate the surface integral \[ \iint_{S} \vec{F} \cdot d \vec{S} \text {, } \] where \( \vec{F}=y \vec{\imath}+x \vec{\jmath}+z \vec{k} \), and the normal to \( S \) is pointing away from the \( x y \)-plane.

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}

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

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

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l } { x } & { - 0.001 } & { 0 } & { 0.0011 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

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