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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Question
Prove each identity using the definitions of the hyperbolic functions
![The image shows the mathematical expression for the hyperbolic tangent function, denoted as \(\tanh x\). The formula is as follows:
\[
\tanh x = \frac{e^{2x} - 1}{e^{2x} + 1}
\]
This function describes the hyperbolic tangent of \(x\) in terms of the exponential function \(e\), which is a crucial function in calculus and complex analysis. The hyperbolic tangent is used in various mathematical, engineering, and physics applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafc613be-7d86-4fc7-875f-926e475289ca%2F12a9d279-6946-4e0b-a6f2-121aef22a526%2Fzepvsk4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows the mathematical expression for the hyperbolic tangent function, denoted as \(\tanh x\). The formula is as follows:
\[
\tanh x = \frac{e^{2x} - 1}{e^{2x} + 1}
\]
This function describes the hyperbolic tangent of \(x\) in terms of the exponential function \(e\), which is a crucial function in calculus and complex analysis. The hyperbolic tangent is used in various mathematical, engineering, and physics applications.
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