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

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Logarithmic Forms of Inverse Hyperbolic Functions
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What is the logarithmic form of sinh1x\sinh^{-1} x?

ln(x+x2+1)\ln(x + \sqrt{x^2 + 1})

What is the logarithmic form of cosh1x\cosh^{-1} x?

ln(x+x21)\ln(x + \sqrt{x^2 - 1})

What is the logarithmic form of tanh1x\tanh^{-1} x?

12ln(1+x1x)\frac{1}{2} \ln\left(\frac{1+x}{1-x}\right)

What is the domain of cosh1x\cosh^{-1} x?

x1x \geq 1

What is the domain of tanh1x\tanh^{-1} x?

x<1|x| < 1

What is the domain of sinh1x\sinh^{-1} x?

xRx \in \mathbb{R}

What is the value of sinh1(2)\sinh^{-1}(2) in exact form?

ln(2+5)\ln(2 + \sqrt{5})

Which square root term appears in cosh1x\cosh^{-1} x but NOT in sinh1x\sinh^{-1} x?

x21\sqrt{x^2 - 1}

In deriving sinh1x\sinh^{-1} x, what quadratic in eye^y is formed?

(ey)22xey1=0(e^y)^2 - 2xe^y - 1 = 0

What is the value of tanh1(0.5)\tanh^{-1}(0.5) in exact form?

12ln(3)\frac{1}{2} \ln(3)

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