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(a) Construct a forward difference table for the above data. (b) (i) Use the table presented in (a), along with Newton's forward difference formula, to approximate f(7) with a polynomial of degree 3, P3(r). Start with a = 1. (ii) Estimate the error in the approximation in (b)(i).

(a) Construct a forward difference table for the above data. (b) (i) Use the table presented in (a), along with Newton's forward difference formula, to approximate f(7) with a polynomial of degree 3, P3(r). Start with a = 1. (ii) Estimate the error in the approximation in (b)(i).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with a and b

(a) Construct a forward difference table for the above data. (b) (i) Use the table presented in (a), along with Newton's forward difference formula, to approximate f(7) with a polynomial of degree 3, P3(r). Start with zo = 1. (ii) Estimate the error in the approximation in (b) (i). 15 DAARNALIA
Transcribed Image Text:(a) Construct a forward difference table for the above data. (b) (i) Use the table presented in (a), along with Newton's forward difference formula, to approximate f(7) with a polynomial of degree 3, P3(r). Start with zo = 1. (ii) Estimate the error in the approximation in (b) (i). 15 DAARNALIA
The table time (x₂) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease at intervals of 1 day over a period of 6 days. Here i = 0, 1, 2,..., 5 and the quantities zo=1 and yo = 32, respectively, represent the end of the first day of testing for the disease, and number of positive tests conducted by the end of that day. (Note: r; represents the end of a testing day, where the values of r, are as tabulated, while Yi represents the number of positive tests conducted by the end of day ₁.)
Transcribed Image Text:The table time (x₂) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease at intervals of 1 day over a period of 6 days. Here i = 0, 1, 2,..., 5 and the quantities zo=1 and yo = 32, respectively, represent the end of the first day of testing for the disease, and number of positive tests conducted by the end of that day. (Note: r; represents the end of a testing day, where the values of r, are as tabulated, while Yi represents the number of positive tests conducted by the end of day ₁.)
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