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Calculus with hyperbolic functionsAQA A-Level Further Maths: Flashcards

What these 14 flashcards ask

  • Differentiate \sinh x.
  • Differentiate \cosh x.
  • Differentiate \tanh x.
  • Differentiate \operatorname{sech}x.
  • Differentiate \coth x.
  • Find \int\cosh kx\,dx.
  • Find \int\operatorname{sech}^2x\,dx.
  • Find \int\tanh x\,dx.
  • What is \cosh(\ln a)?
  • State \int\frac{1}{\sqrt{x^2+a^2}}\,dx.
  • State \int\frac{1}{\sqrt{x^2-a^2}}\,dx for xa.
  • Which substitution suits \sqrt{x^2+a^2}?
  • Which substitution suits \sqrt{x^2-a^2}?
  • What do you do with x^2-6x+5 inside a square root?

Exam questions on Calculus with hyperbolic functions

  1. The function ff is defined by f(x)=cosh⁡2xf(x)=\cosh 2x.
    Find the exact value of ∫0ln⁡2f(x) dx\int_0^{\ln2}f(x)\,dx.2 marks
  2. The function gg is defined by g(x)=tanh⁡xg(x)=\tanh x for all real xx.
    Find the exact gradient of the curve y=g(x)y=g(x) at the point where x=ln⁡3x=\ln3.2 marks
  3. A curve has equation y=2cosh⁡x−3sinh⁡xy=2\cosh x-3\sinh x.
    Show that the curve has no stationary points.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).