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Match the following to create correct hyperbolic function identities and inverse hyperbolic function definitions. 1 – tanh r csch X coth²x - - 1 1 coth x coshæ + sinh a. csch² x b. sech² x c. - /mn (2+1) C. -In 1 1 2. ln ( = 2 + √ [ +2²³) d. In - |x| e. e

Match the following to create correct hyperbolic function identities and inverse hyperbolic function definitions. 1 – tanh r csch X coth²x - - 1 1 coth x coshæ + sinh a. csch² x b. sech² x c. - /mn (2+1) C. -In 1 1 2. ln ( = 2 + √ [ +2²³) d. In - |x| e. e

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Hyperbolic Function Matching Exercise** Match the following expressions to create correct identities and inverse hyperbolic function definitions: 1. \(1 - \tanh^2 x\) 2. \(\csch^{-1} x\) 3. \(\coth^2 x - 1\) 4. \(\coth^{-1} x\) 5. \(\cosh x + \sinh x\) **Options:** a. \(\csch^2 x\) b. \(\sech^2 x\) c. \(\frac{1}{2} \ln\left(\frac{x+1}{x-1}\right)\) d. \(\ln\left(\frac{1}{x} + \frac{\sqrt{1 + x^2}}{|x|}\right)\) e. \(e^x\)
Transcribed Image Text:**Hyperbolic Function Matching Exercise** Match the following expressions to create correct identities and inverse hyperbolic function definitions: 1. \(1 - \tanh^2 x\) 2. \(\csch^{-1} x\) 3. \(\coth^2 x - 1\) 4. \(\coth^{-1} x\) 5. \(\cosh x + \sinh x\) **Options:** a. \(\csch^2 x\) b. \(\sech^2 x\) c. \(\frac{1}{2} \ln\left(\frac{x+1}{x-1}\right)\) d. \(\ln\left(\frac{1}{x} + \frac{\sqrt{1 + x^2}}{|x|}\right)\) e. \(e^x\)
A population of bacteria is growing according to the equation \( P(t) = 1650e^{0.21t} \), where \( t \) is in hours. Estimate when the population will reach 5817. Round to one decimal place. \[ t = \text{________} \text{ hours} \]
Transcribed Image Text:A population of bacteria is growing according to the equation \( P(t) = 1650e^{0.21t} \), where \( t \) is in hours. Estimate when the population will reach 5817. Round to one decimal place. \[ t = \text{________} \text{ hours} \]
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