Concept explainers
(a)
To Find: The interval that is one unit length in which the polynomial function is guaranteed to have a zero.
(a)
Answer to Problem 92E
The required interval is
Explanation of Solution
Given:
The given function is
Calculation:
Consider the given function is,
Table of values for the above function is shown in Table 1
Table
-5 | 378 |
-4 | 99 |
-3 | -6 |
-2 | -21 |
-1 | -6 |
0 | 3 |
1 | -6 |
0 | -21 |
3 | -6 |
4 | 99 |
The change of sign shows the interval as,
(b)
To Find: The adjustment for the table approximate the zeroes of the function to the nearest tenth.
(b)
Answer to Problem 92E
The values are
Explanation of Solution
Consider the given function is,
The adjusted table to approximate the first zero
Table 1
-3.20 | 5.4576 |
-3.19 | 4.7920112 |
-3.18 | 4.1366338 |
-3.17 | 3.4913912 |
-3.16 | 2.8562074 |
-3.15 | 2.2310062 |
-3.14 | 1.6157122 |
-3.13 | 1.01029496 |
-3.11 | -0.17148159 |
Approximate the table to approximate the first zero
Table 2
-3.20 | 0.41454336 |
-3.119 | 0.35550644 |
-3.118 | 0.29656626 |
-3.117 | 0.23772274 |
-3.116 | 0.17897582 |
-3.115 | 0.1203254 |
-3.114 | 0.061771424 |
-3.113 | 0.0033138114 |
-3.112 | -0.055047512 |
-3.111 | -0.11331262 |
-3.110 | -0.17148159 |
From above the value of
Repeating the process for the three zeroes the result is,
Thus, the values are
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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