AQA FP2 2013 June — Question 2

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
TopicHyperbolic functions

2
    1. Sketch on the axes below the graphs of \(y = \sinh x\) and \(y = \cosh x\).
    2. Use your graphs to explain why the equation $$( k + \sinh x ) \cosh x = 0$$ where \(k\) is a constant, has exactly one solution.
  1. A curve \(C\) has equation \(y = 6 \sinh x + \cosh ^ { 2 } x\). Show that \(C\) has only one stationary point and show that its \(y\)-coordinate is an integer.
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