(a)
To complete the tables.
(a)
Answer to Problem 9E
The completed tables are as follows:
Table 1
| |
1.5 | |
1.9 | |
1.99 | |
1.999 | |
Table 2
| |
2.5 | |
2.1 | |
2.01 | |
2.001 | |
Table 3
| |
10 | |
50 | |
100 | |
1000 | |
Table 4
| |
| |
| |
| |
| |
Explanation of Solution
Given information:
The rational function is
Calculation:
To complete each table, substitute, each value of
Therefore, the tables are obtained as:
Table 1
| |
1.5 | |
1.9 | |
1.99 | |
1.999 | |
Table 2
| |
2.5 | |
2.1 | |
2.01 | |
2.001 | |
Table 3
| |
10 | |
50 | |
100 | |
1000 | |
Table 4
| |
| |
| |
| |
| |
(b)
To describe the behaviour of the function near its vertical asymptote.
(b)
Answer to Problem 9E
The behaviour of the function near its vertical asymptote is as
Explanation of Solution
Given information:
The rational function is
The
Use table 1 and table 2 to identify the behaviour of the function for
Table 1
| |
1.5 | |
1.9 | |
1.99 | |
1.999 | |
Table 2
| |
2.5 | |
2.1 | |
2.01 | |
2.001 | |
From the above table shown above, it can be concluded that as
Hence,
The behaviour of the function near its vertical asymptote is as
(c)
To find the horizontal asymptote.
(c)
Answer to Problem 9E
The horizontal asymptote is the line
Explanation of Solution
Given information:
The rational function is
The horizontal asymptote is the value that
Table 3
| |
10 | |
50 | |
100 | |
1000 | |
Table 4
| |
| |
| |
| |
| |
From the above table shown above, it can be concluded that as
Hence,
The horizontal asymptote is the line
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th 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