Concept explainers
a.
To find: the area A of the window as a function of x .
a.
Answer to Problem 84E
Explanation of Solution
Calculation:
A window of perimeter 16 feet is constructed by adjoining a semicircle to the top of an ordinary rectangular window is given below:
The perimeter of the window is:
Perimeter = Length of three sides of the rectangle + arc of the semi circle
It is given that the perimeter of window is16. This gives that,
Now area of the window is,
Area = Area of rectangle + Area of semi circle
Substitute
Conclusion The area A of the window as a function of x is
b.
To find: the dimensions that produce maximum enclosed area.
b.
Answer to Problem 84E
The dimensions that produce maximum enclosed area are
Explanation of Solution
Given:
The area A of the window as a function of x is
Concept Used:
For the function
When
When
Calculation:
Now compare the given function
Clearly
So by the above definition, f has a maximum at
So, the dimensions that produce maximum enclosed area is,
From part (a),
Conclusion:
The dimensions that produce maximum enclosed area are
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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