Concept explainers
If 4x – 9 ≤ f(x)≤ x2 – 4x + 7 for x ≥ 0, find
To evaluate: The limit value of the function
Answer to Problem 29E
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 4, the inequality becomes,
Let
Obtain the limit value of as x approaches 4 of the function
Obtain the limit value of as x approaches 4 of the function
If
That is,
Thus, the limit value of the function
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