Concept explainers
If 2x – 1 ≤ f(x) ≤ x2 for 0 < x < 3, find
To evaluate: The limit value of the function
Answer to Problem 21RE
The limit value of the function
Explanation of Solution
Given:
The inequality,
Limit Laws:
Suppose that c is a constant and the limits
Limit law 1:
Limit law 2:
Limit law 3:
Limit law 7:
Limit law 8:
Limit law 9:
Theorem used: The Squeeze Theorem
“If
Calculation:
Apply the Squeeze Theorem and obtain a function g smaller than
The given inequality becomes,
When the limit x approaches to 1, the inequality becomes,
Let
Obtain the limit value of the function
Obtain the limit value of the function
If
That is,
Thus, the limit value of the function
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
Precalculus (10th Edition)
Precalculus: Mathematics for Calculus - 6th Edition
Thomas' Calculus: Early Transcendentals (14th Edition)
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Precalculus: A Unit Circle Approach (3rd Edition)
Calculus: Early Transcendentals (3rd 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