Inverse hyperbolic functions

Inverse hyperbolic functions Quiz

Spec H3–H4 · AQA A-Level Further Maths: Quiz

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  1. 1. Find the exact value of sinh⁡−11\sinh^{-1}1.

    • A. ln⁡(1+3)\ln\left(1+\sqrt3\right)
    • B. ln⁡2\ln2
    • C. ln⁡(2−1)\ln\left(\sqrt2-1\right)
    • D. ln⁡(1+2)\ln\left(1+\sqrt2\right)

  2. 2. Find the exact value of cosh⁡−154\cosh^{-1}\frac54.

    • A. ln⁡2\ln2
    • B. ln⁡32\ln\frac32
    • C. ln⁡5+414\ln\frac{5+\sqrt{41}}{4}
    • D. ln⁡12\ln\frac12

  3. 3. Find the exact value of tanh⁡−135\tanh^{-1}\frac35.

    • A. ln⁡4\ln4
    • B. ln⁡2\ln2
    • C. 12ln⁡23\frac12\ln\frac{2}{3}
    • D. 12ln⁡85\frac12\ln\frac85

  4. 4. Which formula is correct for tanh⁡−1x\tanh^{-1}x?

    • A. ln⁡(1+x1−x)\ln\left(\frac{1+x}{1-x}\right)
    • B. 12ln⁡(1−x1+x)\frac12\ln\left(\frac{1-x}{1+x}\right)
    • C. 12ln⁡(1+x1−x)\frac12\ln\left(\frac{1+x}{1-x}\right)
    • D. 12ln⁡(x+x2−1)\frac12\ln\left(x+\sqrt{x^2-1}\right)

  5. 5. Given tanh⁡−1x=ln⁡3\tanh^{-1}x=\ln3, find xx.

    • A. 45\frac45
    • B. 34\frac34
    • C. 23\frac23
    • D. 89\frac89

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