To Describe: The Squeeze Theorem
Explanation of Solution
Statement:
Suppose that
Result used: Definition of limits
Let
By the definition of limits, since
Proof:
Let
By the definition of limits, since
Thus,
Similarly, since
Thus,
Since
Choose
Therefore,
So
By the definition of limits
Example:
To prove: The limit of the function
Theorem used: The Squeeze Theorem.
“If
Proof:
First take that
Since computing the limit as x goes to infinity, then assume that
Thus,
Apply the limit that is
Since
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