9 Use l'Hôpital's rule to show that
$$\lim _ { x \rightarrow \infty } \left( x \mathrm { e } ^ { - x } \right) = 0$$
Fully justify your answer.
[0pt]
[4 marks]
| 10 | | Evaluate the improper integral \(\int _ { 0 } ^ { 8 } \ln x \mathrm {~d | | showing the limiting process. |
} | [6 marks] |
\(11 \quad\) The line \(L _ { 1 }\) has equation \(\mathbf { r } = \left[ \begin{array} { l } 2
2
3 \end{array} \right] + \lambda \left[ \begin{array} { c } 2
3
- 1 \end{array} \right]\)
The line \(L _ { 2 }\) has equation \(\mathbf { r } = \left[ \begin{array} { l } 6
4
1 \end{array} \right] + \mu \left[ \begin{array} { c } - 2
1
1 \end{array} \right]\)