(a)
To find: The linearization of the given function and approximate the value of
(a)
Explanation of Solution
Given: the function is
Differentiate the function with respect to
The linear approximation at
Thus,
Now,
Thus,
Therefore,
(b)
To find: The value of
(b)
Explanation of Solution
Given: the function is
The accuracy of
So choose
The graph of
Figure (1)
It is visible from the graph the linear approximation intersects the upper curve at
Therefore, for the accuracy it is required to have
Chapter 3 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