Concept explainers
To guess: The value of
Answer to Problem 19E
The limit of the function is guessed to 5.
Explanation of Solution
Given:
The values of t are
Calculation:
Since t approaches 0, the values
Evaluate the function (correct to 6 decimal places) when
−0.5 | 0.082084999 | −0.91792 | 1.835830 |
−0.1 | 0.60653066 | −0.39347 | 3.934693 |
−0.01 | 0.951229425 | −0.04877 | 4.877057 |
−0.001 | 0.995012479 | −0.00499 | 4.987520 |
−0.0001 | 0.999500125 | −0.0005 | 4.998750 |
Here, the value of
That is,
Evaluate the function (correct to 6 decimal places) when
0.5 | 12.18249396 | 11.18249 | 22.364987 |
0.1 | 1.648721271 | 0.648721 | 6.487212 |
0.01 | 1.051271096 | 0.051271 | 5.127109 |
0.001 | 1.005012521 | 0.005013 | 5.012520 |
0.0001 | 1.000500125 | 0.0005 | 5.001250 |
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 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