Concept explainers
a.
To find: an upper bound for
a.
Answer to Problem 51RE
Explanation of Solution
Given information: Given curve is
Calculation:
Graph the absolute value of it:
From the graph:
b.
To approximate:
b.
Answer to Problem 51RE
Explanation of Solution
Given information:
Calculation:
Calculate values of the function from 0 to
x | f(x) |
0.000000 | 0.000000 |
0.314159 | 0.304122 |
0.628319 | 0.554519 |
0.942478 | 0.723609 |
1.256637 | 0.814030 |
1.570796 | 0.841471 |
1.884956 | 0.814030 |
2.199115 | 0.723609 |
2.513274 | 0.554519 |
2.827433 | 0.304122 |
3.141593 | 0.000000 |
Write out the Simpson’s rule formula with n +1 =11 terms, then fill in the numbers.
For the Simpson’s rule error bounds.
c.
To find: how large should n be to guarantee that the size of the error in using
c.
Answer to Problem 51RE
Explanation of Solution
Given information:
Calculation:
For the error less than 0.00001, solve the Simpson’s error formula for n :
For the Simpson’s Rule, round up to the next whole even number, so :
Chapter 5 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