Sketch the graph of \(y = \tanh x\) and state the equations of its asymptotes.
Use the definitions of \(\sinh x\) and \(\cosh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\) to show that
$$\operatorname { sech } ^ { 2 } x + \tanh ^ { 2 } x = 1$$
Solve the equation \(6 \operatorname { sech } ^ { 2 } x = 4 + \tanh x\), giving your answers in terms of natural logarithms. [0pt]
[5 marks]
\section*{Answer space for question 2}