Concept explainers
To find: The function of the perimeter of the rectangle in terms of the length of one of the sides of rectangle and the function domain.
Answer to Problem 54E
The formula for the function of perimeter of the rectangle in terms of its length is
The domain of the function of the perimeter (P) of the rectangle in terms of its length is
In case of length is to be larger than breadth, the domain of P is
Explanation of Solution
Given:
The area of the rectangle is
Formula used:
Area of the rectangle,
Perimeter of the rectangle,
Calculation:
Let the length of the rectangle be l and the breadth be b. Since the area of the rectangle is
Express the equation (1) in terms of length.
Therefore, the function of perimeter of the rectangle in terms of l is
That is,
Therefore, the function of perimeter of the rectangle in terms of its length is
The domain of P is
In the case of length is to be larger than breadth, the domain of P is
Chapter 1 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