Homework Help is Here – Start Your Trial Now!
Math
Calculus
(a) Use the definitions above to show that d tanh x dr 1 cosh r

(a) Use the definitions above to show that d tanh x dr 1 cosh r

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...
See similar textbooks
Question
6. The "hyperbolic trigonometric functions" are specific combinations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by et +e- cosh r the "hyperbolic sine function" is given by - e sinh x = 2 and the "hyperbolic tangent function" is given by sinh x tanh x = cosh x (a) Use the definitions above to show that d tanh a dx 1 cosh? x (b) The velocity of a water wave with length L moving across a body of water with depth d is given by gL ( 2nd tanh 27 V = L where g represents the acceleration due to gravity (a positive constant). What happens to the velocity as the wave length increases without bound? That is, evaluate lim v Hint: Find lim v² first, and then use that to answer the question above. L00
Transcribed Image Text:6. The "hyperbolic trigonometric functions" are specific combinations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by et +e- cosh r the "hyperbolic sine function" is given by - e sinh x = 2 and the "hyperbolic tangent function" is given by sinh x tanh x = cosh x (a) Use the definitions above to show that d tanh a dx 1 cosh? x (b) The velocity of a water wave with length L moving across a body of water with depth d is given by gL ( 2nd tanh 27 V = L where g represents the acceleration due to gravity (a positive constant). What happens to the velocity as the wave length increases without bound? That is, evaluate lim v Hint: Find lim v² first, and then use that to answer the question above. L00
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS