Concept explainers
To prove: The limit of the function
Explanation of Solution
Theorem used: The Squeeze Theorem
“If
Proof:
It is trivial that, the value of
Thus, the limit of the function does not exist.
Apply the Squeeze Theorem and obtain a function f smaller than
Since the cosine function is lies between
Any inequality remains true when multiplied by a positive number. Since
When the limit x approaches zero, the inequality becomes,
Graph:
Use the online graphing calculator to draw the graph of the function as shown below in Figure 1.
From Figure 1, it is observed that
Let
If
That is,
Hence the required proof is obtained.
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