Concept explainers
(a)
To write: .The function
(a)
Explanation of Solution
The expression for cross-sectional area is obtained as,
Therefore, the function that represent the cross-sectional area of the gutteris
(b)
To write: .The function
(b)
Explanation of Solution
The expression for cross-sectional area is obtained as,
Therefore, the function that represent the volume of one run of gutter in terms of
(c)
To find: The domain of the function
(c)
Explanation of Solution
Given: The function
The domain is calculated as,
Therefore, the domain of the function
(c)
To construct: The table constructing to height and
(c)
Explanation of Solution
Given: The function
The table corresponding to height and volume is shown below.
Table (1)
The maximum volume occurs at height
So,
Therefore, the required table is shown in Table (1) and the dimension that will produce the maximum volume is
(e)
To draw: The graph of
(e)
Explanation of Solution
Given: The function
The graph of the function is shown in figure below.
Figure (1)
The volume is maximum at
The height at which the volume is maximum obtained numerically is
Thus, both the results are same.
Therefore, the graph of the volume function is shown in Figure (1) and the height at which volume is maximum is same from both graph and calculation.
(f)
To find: Whether the change in the length of sheet affect the value of
(f)
Explanation of Solution
Given: The function
Changing the length will change the maximum volume but not the point at which the maximum volume occurs.
Therefore, no the change in the length of sheet will not affect the value of
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