Concept explainers
To prove: The value of
Explanation of Solution
Theorem used:
The Squeeze Theorem
“If
Limit Laws:
Suppose that c is a constant and the limits
Limit law 3:
Limit law 10:
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 sine function lies between
Take the exponential of the inequality,
Any inequality remains true when multiplied by a positive number. Since
When x approaches to zero, the inequality becomes,
Obtain the value of
Obtain the value of
Let
Sketch the graph of the functions
From Figure 1, it is observed that
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