8 Fig. 8 shows the curve \(y = \frac { x } { \sqrt { x + 4 } }\) and the line \(x = 5\). The curve has an asymptote \(l\).
The tangent to the curve at the origin O crosses the line \(l\) at P and the line \(x = 5\) at Q .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{414a6b7f-cd96-4fa0-9521-ebe500bab375-3_643_921_703_573}
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\caption{Fig. 8}
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- Show that for this curve \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x + 8 } { 2 ( x + 4 ) ^ { \frac { 3 } { 2 } } }\).
- Find the coordinates of the point P .
- Using integration by substitution, find the exact area of the region enclosed by the curve, the tangent OQ and the line \(x = 5\).