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Hyperbolic Functions (Edexcel A Level Further Maths: Core Pure): Exam Questions

21 mins3 questions
1
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y space equals space sin space x space sinh space x

Show that fraction numerator straight d to the power of 4 y over denominator straight d x to the power of 4 end fraction equals negative 4 y

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2
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The curve C has equation

y space equals space 31 space sinh space x space minus space 2 space sinh space 2 x space space space space space space space x space element of straight real numbers

Determine, in terms of natural logarithms, the exact x coordinates of the stationary points of C.

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3a
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(a) Prove that

tanh to the power of negative 1 end exponent left parenthesis x right parenthesis equals 1 half space ln open parentheses fraction numerator 1 plus x over denominator 1 minus x end fraction close parentheses space space space space – k space less than space x italic space italic less than italic space k

stating the value of the constant k.

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3b
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(b) Hence, or otherwise, solve the equation

2 x space equals space tanh left parenthesis ln square root of 2 minus 3 x end root right parenthesis

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