(a)
To define: The number e.
(a)
Answer to Problem 3RCC
The number e is
Explanation of Solution
From the definition, e is the number such that
(b)
To express: The number e as a limit.
(b)
Answer to Problem 3RCC
The number e can be expressed as
Explanation of Solution
The expansion of
Substitute 1 for x in
Also observe that,
From equations (1) and (2), it can be concluded that
(c)
To find: The natural logarithmic function
(c)
Explanation of Solution
The derivative of the logarithmic function
(d)
To find: The natural logarithmic function
(d)
Explanation of Solution
The derivative of the natural log:
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