3. (i) Solve
(ii)
$$\frac { 3 } { x } > 4$$
Figure 1 shows a sketch of the curve \(C\) and the straight line \(l\).
The infinite region \(R\), shown shaded in Figure 1, lies in quadrants 2 and 3 and is bounded by \(C\) and \(l\) only.
Given that
- \(\quad l\) has a gradient of 3
- \(C\) has equation \(y = 2 x ^ { 2 } - 50\)
- \(\quad C\) and \(l\) intersect on the negative \(x\)-axis
use inequalities to define the region \(R\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-06_643_652_575_648}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) and the straight line \(l\).
The infinite region \(R\), shown shaded in Figure 1, lies in quadrants 2 and 3 and is bounded by \(C\) and \(l\) only.
Given that
- \(l\) has a gradient of 3
- \(C\) has equation \(y = 2 x ^ { 2 } - 50\)
- \(C\) and \(l\) intersect on the negative \(x\)-axis
use inequalities to define the region \(R\).