Concept explainers
(a)
To estimate: The value of
(a)
Answer to Problem 26E
The value of
Explanation of Solution
Using the graphing calculator, the graph of the function
Zoom the graph towards the point where the graph crosses the y-axis as shown below in Figure 2.
From Figure 2, it is observed that graph of
Since the right hand and the left hand limits are equal, the value of
That is,
Thus, the value of
(b)
To check: The correctness of the answer obtained in part (a) by evaluating the value of
(b)
Explanation of Solution
As x approaches 0, evaluate the function
Evaluate the function (correct to 6 decimal places) for the values of x and get the following table of values.
−0.5 | −1.571428571 | −0.9999998 | 0.318346 |
−0.1 | −0.314285714 | −0.309137252 | 0.318311 |
−0.01 | −0.031428571 | −0.031423398 | 0.318228 |
−0.001 | −0.003142857 | −0.003142852 | 0.318309 |
−0.0001 | −0.000314286 | −0.000314286 | 0.318309 |
0.5 | 1.571428571 | 0.9999998 | 0.318345 |
0.1 | 0.314285714 | 0.309137252 | 0.318311 |
0.01 | 0.031428571 | 0.031423398 | 0.318309 |
0.001 | 0.003142857 | 0.003142852 | 0.318309 |
0.0001 | 0.000314286 | 0.000314286 | 0.318309 |
From the above table, it is observed that the value of
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