AQA FP2 2015 June — Question 2 5 marks

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
Year2015
SessionJune
Marks5
TopicHyperbolic functions

2
  1. Sketch the graph of \(y = \tanh x\) and state the equations of its asymptotes.
  2. Use the definitions of \(\sinh x\) and \(\cosh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\) to show that $$\operatorname { sech } ^ { 2 } x + \tanh ^ { 2 } x = 1$$
  3. 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}

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