Concept explainers
(a)
To evaluate: The limit of the function
(a)
Answer to Problem 5P
The limit of the function does not exist.
Explanation of Solution
Definition used:
Greatest integer function:
Calculation:
Obtain the limit of the function
Let the function
For
By the definition of greatest integer function,
Thus,
For
By the definition of greatest integer function,
Thus,
The left hand limit of the function as x approaches 0 is computed as follows,
The right hand limit of the function as x approaches 0 is computed as follows,
Since the left and right hand limits are not equal.
Thus, the limit of the function
(b)
To evaluate: The limit of the function
(b)
Answer to Problem 5P
The limit of the function is 1.
Explanation of Solution
Result used: Squeeze theorem
“Suppose that
Calculation:
Obtain the limit of the function
Let the function
For
Take the right hand limit of the above inequality as x approaches 0,
Here,
Therefore, by the Squeeze theorem,
For
Take the left hand limit of the above inequality as x approaches 0,
Here,
Therefore, by the Squeeze theorem,
Since the left and right hand limits are equal, the limit exists and equal to 1. That is,
Thus, the limit of the function is 1.
Chapter 2 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