To find: The Taylor series for
Answer to Problem 15E
Theratio test shows that the series converges for all the value of
Explanation of Solution
Given:
Thegiven function is
The series is centred at
Calculation:
Consider the series that is centred at
Then, for the given function as,
Differentiate again,
Differentiate again,
Differentiate again,
The differentiation continues in this way.
Then, the series is,
Then substitute
Consider
Thus, the ratio test shows that the series converges for all the value of
Chapter 8 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