Concept explainers
To find: The limit of the function
Answer to Problem 8RE
The limit of the function is
Explanation of Solution
Formula used:
Direct substitution property:
If f is a polynomial or a rational function and a is in the domain of f, then
Difference of cubes formula:
Difference of squares formula:
Fact 1:
If
Given:
Let
Note 1:
The direct substitution method is not applicable for the function
Note 2:
“The limit may be infinite or it may be some finite value when both the numerator and the denominator approach 0.”
Calculation:
By note 2, consider the limit t approaches 2 but
Simplify
Apply the difference of squares formula in the denominator,
Apply the difference of cubes formula in the numerator,
Since the limit of t approaches to 2 but not equal to 2, cancel the common term
By fact 1, if
Apply the direct substitution property on the limit function.
Thus, the limit of the function is
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