The shear stresses, in kilopascals (kPa), of nine specimens taken at various depths in a clay stratum are listed below: 1.9 3.1 4.2 5.1 5.8 7.1 8.1 9.3 10 Depth (m) Stress (kPa) 14.4 28.7 19.2 43.1 33.7 52.7 71.8 62.2 76.6 a) Use Newton's third-order polynomial interpolation to find the stress at depth of 4.5 m to the best possible accuracy (Note: choose the best data that will minimize the error). b) Using the function found in part (a), determine the absolute relative approximate error in estimating the value of stress when the depth 5.8 m c) Find the absolute relative approximate error if the second order polynomial approximation is used instead of the third order for part (a).
The shear stresses, in kilopascals (kPa), of nine specimens taken at various depths in a clay stratum are listed below: 1.9 3.1 4.2 5.1 5.8 7.1 8.1 9.3 10 Depth (m) Stress (kPa) 14.4 28.7 19.2 43.1 33.7 52.7 71.8 62.2 76.6 a) Use Newton's third-order polynomial interpolation to find the stress at depth of 4.5 m to the best possible accuracy (Note: choose the best data that will minimize the error). b) Using the function found in part (a), determine the absolute relative approximate error in estimating the value of stress when the depth 5.8 m c) Find the absolute relative approximate error if the second order polynomial approximation is used instead of the third order for part (a).
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
Topic Video
Question
It's urgent please solve quickly
Transcribed Image Text:The shear stresses, in kilopascals (kPa), of nine specimens taken at various depths in a clay
stratum are listed below:
10
Depth (m)
Stress (kPa) 14.4 28.7
1.9
3.1
4.2
5.1
5.8
7.1
8.1
9.3
19.2
43.1
33.7
52.7
71.8
62.2
76.6
a) Use Newton's third-order polynomial interpolation to find the stress at depth of 4.5 m
to the best possible accuracy (Note: choose the best data that will minimize the error).
b) Using the function found in part (a), determine the absolute relative approximate error
in estimating the value of stress when the depth = 5.8 m
c) Find the absolute relative approximate error if the second order polynomial
approximation is used instead of the third order for part (a).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
