1. Consider the following data: X -0.5 -0.25 0 f (x) -0.0247500 0.3349375 1.1010000 f'(x) 0.7510000 2.1890000 4.0020000 a) Determine the Hermite polynomial approximation at x =-- 1313 b) The data was generated using the function f(x) = x³ +4.001x² +4.002x + 1.101. Calculate the absolute error for the approximation in part (a).
1. Consider the following data: X -0.5 -0.25 0 f (x) -0.0247500 0.3349375 1.1010000 f'(x) 0.7510000 2.1890000 4.0020000 a) Determine the Hermite polynomial approximation at x =-- 1313 b) The data was generated using the function f(x) = x³ +4.001x² +4.002x + 1.101. Calculate the absolute error for the approximation in 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
Question
![1. Consider the following data:
X
-0.5
-0.25
0
f(x)
-0.0247500
0.3349375
1.1010000
X
1
a) Determine the Hermite polynomial approximation at x =-
b)
The data was generated using the function ƒ(x) = x³ + 4.001x² +4.002x + 1.101. Calculate the absolute error
for the approximation in part (a).
2. Use the following data and the knowledge that the first five derivatives of f are bounded on [1,5] by 2, 3, 6, 12 and
23, respectively, to approximate ƒ'(3) as accurately as possible. Find a bound for the error.
1
f(x) 2.4142
2
f'(x)
0.7510000
2.1890000
4.0020000
2.6734
3
2.8974
4
3.0976
5
3.2804](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33538a01-f169-4bb5-a2ec-9db4f92608fd%2F527a48b3-ffec-4a80-b121-0da95eef24ac%2Fxxegkp8_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the following data:
X
-0.5
-0.25
0
f(x)
-0.0247500
0.3349375
1.1010000
X
1
a) Determine the Hermite polynomial approximation at x =-
b)
The data was generated using the function ƒ(x) = x³ + 4.001x² +4.002x + 1.101. Calculate the absolute error
for the approximation in part (a).
2. Use the following data and the knowledge that the first five derivatives of f are bounded on [1,5] by 2, 3, 6, 12 and
23, respectively, to approximate ƒ'(3) as accurately as possible. Find a bound for the error.
1
f(x) 2.4142
2
f'(x)
0.7510000
2.1890000
4.0020000
2.6734
3
2.8974
4
3.0976
5
3.2804
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 4 steps with 8 images
Similar questions
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,
