Hyperbolic Functions 1 (AQA A-Level Further Maths): Quizzes

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Hyperbolic Functions 1
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What is the definition of sinh⁡x\sinh x?

ex−e−x2\frac{e^x - e^{-x}}{2}

What is the definition of cosh⁡x\cosh x?

ex+e−x2\frac{e^x + e^{-x}}{2}

What is the value of cosh⁡0\cosh 0?

11

What is the minimum point of the graph y=cosh⁡xy = \cosh x?

(0,1)(0, 1)

Which property does the graph of y=sinh⁡xy = \sinh x have?

Rotational symmetry about the origin

What are the horizontal asymptotes of y=tanh⁡xy = \tanh x?

y=1y = 1 and y=−1y = -1

What is the fundamental hyperbolic identity?

cosh⁡2x−sinh⁡2x≡1\cosh^2 x - \sinh^2 x \equiv 1

What is the logarithmic form of sinh⁡−1x\sinh^{-1} x?

ln⁡(x+x2+1)\ln(x + \sqrt{x^2 + 1})

What is the domain restriction for cosh⁡−1x\cosh^{-1} x?

x≥1x \geq 1

The graph of y=2+cosh⁡xy = 2 + \cosh x has its minimum at which point?

(0,3)(0, 3)

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