I. The following table of experimental data is provided: 2 3 22.2 74 X₁ f(x₁) 4 176.8 5 348.6 a- Construct the table of the divided differences and write the third degree polynomial that interpolates the given data [Write the polynomial P(x) under the form: P(x) = f(xo) + (x-xo)f(x0, x₁) + (x − xo)(x- - *₁)f(x0, x₁, x₂) + (x-xo)(x-x₁)(x-x₂)f(x0, x₁, x₂, x3)] b- Find the least square straight line y = ao + a,x that minimizes the vertical differences. c- Find the approximation curve y = aebx (a > 0) that minimizes the vertical differences. Write the results in the following table:
I. The following table of experimental data is provided: 2 3 22.2 74 X₁ f(x₁) 4 176.8 5 348.6 a- Construct the table of the divided differences and write the third degree polynomial that interpolates the given data [Write the polynomial P(x) under the form: P(x) = f(xo) + (x-xo)f(x0, x₁) + (x − xo)(x- - *₁)f(x0, x₁, x₂) + (x-xo)(x-x₁)(x-x₂)f(x0, x₁, x₂, x3)] b- Find the least square straight line y = ao + a,x that minimizes the vertical differences. c- Find the approximation curve y = aebx (a > 0) that minimizes the vertical differences. Write the results in the following table:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![1. The following table of experimental data is provided:
2
3
22.2
74
X₁
f(x₁)
4
176.8
5
348.6
a- Construct the table of the divided differences and write the third degree polynomial that
interpolates the given data
[Write the polynomial P(x) under the form: P(x) = f(x) + (x-xo)ƒ (x0, x₁) + (x − xo)(x -
x₁)f(x0, x₁, x₂)+(x-xo)(x-x₁)(x-x₂)f(x0, x₁, x₂, x3)]
b- Find the least square straight line y = ao + a,x that minimizes the vertical differences.
c- Find the approximation curve y = aebx (a > 0) that minimizes the vertical differences.
Write the results in the following table:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb02ea9ab-2e6c-47ec-9bf7-dc8753f7299d%2Fc16ce57f-f06a-4959-ba49-be0ac307024d%2Fdjjvobq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The following table of experimental data is provided:
2
3
22.2
74
X₁
f(x₁)
4
176.8
5
348.6
a- Construct the table of the divided differences and write the third degree polynomial that
interpolates the given data
[Write the polynomial P(x) under the form: P(x) = f(x) + (x-xo)ƒ (x0, x₁) + (x − xo)(x -
x₁)f(x0, x₁, x₂)+(x-xo)(x-x₁)(x-x₂)f(x0, x₁, x₂, x3)]
b- Find the least square straight line y = ao + a,x that minimizes the vertical differences.
c- Find the approximation curve y = aebx (a > 0) that minimizes the vertical differences.
Write the results in the following table:
Transcribed Image Text:do
Onsider the integral /
m
a₁
(6x² + 3x²)dr
a₂
a3
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