Concept explainers
(a)
Average temperature when endpoint values are doubled.
(a)
Answer to Problem 21E
The average temperature is 70.08 when endpoint values are doubled.
Explanation of Solution
Given information:
In the Trapezoidal rule,
Except endpoint values, every function value is doubled.
According to Trapezoidal rule,
Substitute the values,
Now,
When the endpoint values of 63 and 55 are doubled,
Thus,
The average temperature:
(b)
Significance for not to double the endpoint values if the average temperature is considered over the entire 12 − hour period.
(b)
Answer to Problem 21E
It does not make any sense to double the endpoint values.
Explanation of Solution
Given information:
Average temperature is considered over 12 − hour period.
From Part (a) result,
We came to know that
The average temperature changes when the endpoints are doubled.
After doubling the endpoint values,
The error in first and last trapezoids increases.
Therefore,
It does not make any sense to double the endpoint values.
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus & Its Applications (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th 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