Concept explainers
To evaluate: The value of
Answer to Problem 12E
The limit of the function does not exist.
Explanation of Solution
Limit Laws:
Suppose that c is a constant and the limits
Limit law 2:
Limit law 7:
Limit law 8:
Limit law 9:
Theorem 1:
“
Reason:
The limit of the denominator is zero, which is calculated as follows.
The quotient law cannot be used as the denominator of the function tends to zero when
Let
Simplify
Factorize the denominator
Substitute
Take the common terms out from the numerator,
Cancel the common terms from both the numerator and the denominator,
Thus,
By theorem 1,
Thus, the limit of the function does not 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