   Chapter 3.11, Problem 20E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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

#### A sample with a mean of M = 8 has X = 56. How many scores are in the sample?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 19-24, find the functions f + g, f g, fg, and fg. 24. f(x) = x2 + 1; g(x) = x+1

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

#### In Problems 19-44, factor completely. 44.

Mathematical Applications for the Management, Life, and Social Sciences 