   Chapter 3.11, Problem 20E

Chapter
Section
Textbook Problem

If x = 12 13 find the values of the other hyperbolic functions at x.

To determine

To find: The values of the other hyperbolic functions at x,

Explanation

Given:

The value tanhx=1213.

Formula used:

The hyperbolic functions are sinhx=exex2and coshx=ex+ex2.

Calculation:

The definition of the hyperbolic tangent function is, tanhx=sinhxcoshx.

Since sinhx=exex2and coshx=ex+ex2, the hyperbolic tangent function is tanhx=exexex+ex

Substitute tanhx=exexex+ex in 1+tanhx1tanhx,

1+tanhx1tanhx=1+exexex+ex1exexex+ex=ex+ex+exexex+exex+ex=2ex2ex=e2x

Thus, the values 1+tanhx1tanhx=e2x.

Substitute the value tanhx=1213 in 1+tanhx1tanhx=e2x,

1+121311213=e2x13+1213131213=e2x25=e2xex=5

The definition of the hyperbolic sine function is, sinhx=exex2

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Evaluate i=1n(2i+2i).

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 75-98, perform the indicated operations and/or simplify each expression. 78. 3(2a b) 4(b 2a)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Compute C7,7.

Understanding Basic Statistics

Find each product: (42a)(12a3b)

Elementary Technical Mathematics

Evaluate the integrals in Problems 1-26.

Mathematical Applications for the Management, Life, and Social Sciences

Calculate y'. 12. y = (arcsin 2x)2

Single Variable Calculus: Early Transcendentals

01e2xdx= a) 2e2 1 b) `e2 1 c) 12e2 d) 12(e21)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

For

Study Guide for Stewart's Multivariable Calculus, 8th

Identify possible sources and use them to identify a topic area for research.

Research Methods for the Behavioral Sciences (MindTap Course List) 