Concept explainers
To describe: The limit can fail to exist in several ways.
Explanation of Solution
The limit fails to exist for several ways are:
- (i) The left and right limits are not equal
Graph:
Example:
Here
(ii) When the function approach a infinity large value the limit fails to exits.
Graph:
Example:
In the graph
particular value.
(iii) When the function doesn’t approach a particular value then the limit of the function doesn’t exist
Graph:
Example:
The function starts the oscillations faster. The function oscillates between 1 and –1.
(iv) When x-value is approaching the endpoint of a closed interval the limit of the function doesn’t exist.
Graph:
Example:
In the graph the function is only defined for x-values to the right of 0, but x doesn’t approach from the left. So the both sides are not equal then the limit of the function doesn’t exist.
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