Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The table time (z.) 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: z, represents the end of a testing day, where the values of z, are as tabulated, while y, represents the number of positive tests conducted by the end of day x..) Page 4 of 5 (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, P₁(a). Start with a = 1. (ii) Estimate the error in the approximation in (b)(i).

The table time (z.) 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: z, represents the end of a testing day, where the values of z, are as tabulated, while y, represents the number of positive tests conducted by the end of day x..) Page 4 of 5 (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, P₁(a). 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
See similar textbooks
icon
Related questions
Question
Please answer the first 3 questions
Question 3: Instruction: Apply one decimal place rounding to calculations where applicable. The table u time (z.) 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: az, represents the end of a testing day, where the values of x, are as tabulated, while y represents the number of positive tests conducted by the end of day x..) Page 4 of 5 (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 = 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, Qa(r). Start with ₁ = 6. (ii) Estimate the error in the approximation in (c) (i). (d) State whether P3(x) and Q3(r) give over or under approximations for f(7).
Transcribed Image Text:Question 3: Instruction: Apply one decimal place rounding to calculations where applicable. The table u time (z.) 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: az, represents the end of a testing day, where the values of x, are as tabulated, while y represents the number of positive tests conducted by the end of day x..) Page 4 of 5 (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 = 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, Qa(r). Start with ₁ = 6. (ii) Estimate the error in the approximation in (c) (i). (d) State whether P3(x) and Q3(r) give over or under approximations for f(7).
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS