The table time (₁) 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 to = 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 a, are as tabulated, while y represents the number of positive tests conducted by the end of day x₁.)
The table time (₁) 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 to = 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 a, are as tabulated, while y represents the number of positive tests conducted by the end of day x₁.)
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 hell with A,B and C
Transcribed Image Text:The table
time (xi)
1
2
infections (y = f(x)) 32 37 34
3 4 5 6
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 To = 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 ri.)
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(x). Start with zo = 1.
(ii) Estimate the error in the approximation in (b)(i).
(c) (i) Use the table presented in (a), along with Newton's backward difference formula, to
approximate f(7) with a polynomial of degree 3, Q3(z). Start with z₁ = 6.
(ii) Estimate the error in the approximation in (c) (i).
(d) State whether P3(r) and Q3(z) give over or under approximations for f(7).
DE
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