Concept explainers
To guess: The limit of the function
Answer to Problem 17E
The limit of the function is guessed to 0.5.
Explanation of Solution
Given:
The values of x are
Calculation:
Since x approaches 3, the values
Evaluate the function (correct to 6 decimal places) when
3.1 | 0.31 | 0.61 | 0.508197 |
3.05 | 0.1525 | 0.3025 | 0.504132 |
3.01 | 0.0301 | 0.0601 | 0.500832 |
3.001 | 0.003001 | 0.006001 | 0.500083 |
3.0001 | 0.0003 | 0.0006 | 0.500008 |
Here, the value of
That is,
Evaluate the function (correct to 6 decimal places) when
2.9 | −0.29 | −0.59 | 0.491525 |
2.95 | −0.1475 | −0.2975 | 0.495798 |
2.99 | −0.0299 | −0.0599 | 0.499165 |
2.999 | −0.003 | −0.006 | 0.499917 |
2.9999 | −0.0003 | −0.0006 | 0.499992 |
Here, the value of
That is,
Since the right hand limit and the left hand limits are the same,
Therefore, the limit of the function is guessed to 0.5.
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