Concept explainers
To show: The limit of the function
Explanation of Solution
Theorem used: The Squeeze Theorem
“If
Proof:
Apply the Squeeze Theorem and obtain a function f smaller than
Since the cosine function is lies between
Let
Any inequality remains true when multiplied by a positive number. Since
When the limit x approaches to zero, the inequality becomes,
Graph:
Sketch the graph of the function by using the online graphing calculator as shown below in Figure (1).
From the graph, it is observed that
If
That is,
Hence showed.
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