Hyperbolic Functions & Graphs (Edexcel A-Level Further Mathematics): Quizzes

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Hyperbolic Functions & Graphs
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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}

Which expression is equivalent to tanh⁡x\tanh x?

ex−e−xex+e−x\frac{e^x - e^{-x}}{e^x + e^{-x}}

What is the range of cosh⁡x\cosh x?

[1,∞)[1, \infty)

What is the range of tanh⁡x\tanh x?

(−1,1)(-1, 1)

Which symmetry property does sinh⁡x\sinh x satisfy?

sinh⁡(−x)=−sinh⁡(x)\sinh(-x) = -\sinh(x)

Which symmetry property does cosh⁡x\cosh x satisfy?

cosh⁡(−x)=cosh⁡(x)\cosh(-x) = \cosh(x)

What are the horizontal asymptotes of tanh⁡x\tanh x?

y=−1y = -1 and y=1y = 1

What is the minimum value of cosh⁡x\cosh x?

11

Through which point does the graph of sinh⁡x\sinh x pass?

(0,0)(0, 0)

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