9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-30_707_1034_251_456}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the curve with equation
$$y = \tan x \quad - 2 \pi \leqslant x \leqslant 2 \pi$$
The line \(l\), shown in Figure 4, is an asymptote to \(y = \tan x\)
- State an equation for \(l\).
A copy of Figure 4, labelled Diagram 1, is shown on the next page.
- On Diagram 1, sketch the curve with equation
$$y = \frac { 1 } { x } + 1 \quad - 2 \pi \leqslant x \leqslant 2 \pi$$
stating the equation of the horizontal asymptote of this curve.
- Hence, giving a reason, state the number of solutions of the equation
- State the number of solutions of the equation \(\tan x = \frac { 1 } { x } + 1\) in the region
- \(0 \leqslant x \leqslant 40 \pi\)
- \(- 10 \pi \leqslant x \leqslant \frac { 5 } { 2 } \pi\)
$$\begin{aligned}
& \qquad \tan x = \frac { 1 } { x } + 1
& \text { in the region } - 2 \pi \leqslant x \leqslant 2 \pi
\end{aligned}$$"
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-31_725_1047_1078_447}
\captionsetup{labelformat=empty}
\caption{Diagram 1}
\end{figure}
\includegraphics[max width=\textwidth, alt={}]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-32_2644_1837_118_114}