Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor expansion of f (x) around x, in the region [x¡-1,X¡+1] and the three-point formulas for the first-order and second-order derivatives. Show that the contribution of the last slice is also correctly given by the formulas in the above discussion.
Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor expansion of f (x) around x, in the region [x¡-1,X¡+1] and the three-point formulas for the first-order and second-order derivatives. Show that the contribution of the last slice is also correctly given by the formulas in the above discussion.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![1. Develop a program that can calculate the integral with a given integrand f(x) in the
region [a, b] by the Simpson rule with nonuniform data points. Check its accuracy with
the integral e*dx with x, = jhei“, where h and a are small constants.
2. Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor
expansion of f (x) around x, in the region [x;-1, X¡+1] and the three-point formulas for
the first-order and second-order derivatives. Show that the contribution of the last
slice is also correctly given by the formulas in the above discussion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5514f31f-32a7-4199-a100-f1af4da1c391%2Fd28904ee-ed64-458c-904e-f18980353260%2Ffpbq06a_processed.png&w=3840&q=75)
Transcribed Image Text:1. Develop a program that can calculate the integral with a given integrand f(x) in the
region [a, b] by the Simpson rule with nonuniform data points. Check its accuracy with
the integral e*dx with x, = jhei“, where h and a are small constants.
2. Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor
expansion of f (x) around x, in the region [x;-1, X¡+1] and the three-point formulas for
the first-order and second-order derivatives. Show that the contribution of the last
slice is also correctly given by the formulas in the above discussion.
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