Concept explainers
To find: The explanation terms of the geometry why the instantaneous rate of change of the area with respect to radius should equal the circumference.
Answer to Problem 49E
The explanation terms of the geometry why the instantaneous rate of change of the area with respect to radius should equal the circumference is obtained.
Explanation of Solution
Given Data:
The area of the circle is
The given function is,
Calculation:
The rate of change of the area with the radius is
Consider that the area of the circle is divided in the smaller segments of the circumference
Chapter 3 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
Precalculus
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus & Its Applications (14th Edition)
Calculus: Early Transcendentals (2nd 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