CAIE A-Level Further Math A2 2.1.4 Hyperbolic Functions Questions

Practise deriving inverse hyperbolic logarithmic forms and related derivatives with Further Mathematics Paper 2 questions.

Exam points

Derive and use logarithmic forms of inverse hyperbolic functions, including inverse tanh and sech derivatives.

[Maximum number: 4]

The curves $C_{1}: y=\cosh x$ and $C_{2}: y=\sinh 2 x$ intersect at the point where x=a.

Find the exact value of a, giving your answer in logarithmic form.

$\cosh a=2 \sinh a \cosh a \Rightarrow \sinh a=\frac{1}{2}$ $a=\sinh ^{-1} \frac{1}{2}=\ln \left(\frac{1}{2}+\sqrt{\frac{1}{4}+1}\right)$ $a=\ln \left(\frac{1}{2}+\frac{1}{2} \sqrt{ } 5\right)$
5a 4

All question bank results loaded

CAIE A-Level Further Math A2 2.1.4 Hyperbolic Functions Questions question 1