Concept explainers
(a)
To find: The linear density at
(a)
Answer to Problem 17E
The linear density at
Explanation of Solution
Given:
The mass of the part of the metal rod which lies between its left end and a point x m away from the right end is
Calculation:
The mass of the metal rod is,
The linear density of the rod is the derivative of the mass and hence
The linear density at
(b)
To find: The linear density at
(b)
Answer to Problem 17E
The linear density at
Explanation of Solution
From part (a), the linear density of the rod is,
The linear density at
The linear density at
(c)
To find: The linear density at
(c)
Answer to Problem 17E
The linear density at
Explanation of Solution
From part (a), the linear density of the rod is,
The linear density at
Notice that the density function is an increasing function. Therefore, the density of the rod is highest at its right end and lowest at its left end.
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning