(d) Use a calculator to estimate the value of f(1.3) = (1.3) In(1.3) to 6 decimal places, and find the actual error |R₂(x)| resulting from using your estimate in part (b). How does this actual error compare to the upper bound on the error that you found in part (c)? Explain.
(d) Use a calculator to estimate the value of f(1.3) = (1.3) In(1.3) to 6 decimal places, and find the actual error |R₂(x)| resulting from using your estimate in part (b). How does this actual error compare to the upper bound on the error that you found in part (c)? Explain.
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
Please solve for part D
![(a) Calculate the quartic (degree 4) Taylor polynomial T4(x) for f(x) = x · ln (x) with center a = 1
directly from the definition of a Taylor polynomial. Show the derivatives and their evaluations.
(b) Use the polynomial T₁ (x) that you found in part (a) to write down a sum of terms that gives an
approximation to the value of f(1.3) = (1.3) In(1.3). Give an answer with 6 decimal places.
(c) Use Taylor's Inequality to find an upper bound on the error |R₂(x)] when T₁(x) is used to
approximate ƒ(1.3) = (1.3) In(1.3). Part of your work will be to find a suitable value for "M."
Give an answer with 6 decimal places.
(d) Use a calculator to estimate the value of ƒ(1.3) = (1.3) · In(1.3) to 6 decimal places, and find the
actual error [R₂(x)| resulting from using your estimate in part (b). How does this actual error compare to
the upper bound on the error that you found in part (c)? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F397485a0-a213-449a-932e-f264adae2773%2F1308d358-d469-4aec-9e07-8336f96c2509%2Fxgswb9m_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Calculate the quartic (degree 4) Taylor polynomial T4(x) for f(x) = x · ln (x) with center a = 1
directly from the definition of a Taylor polynomial. Show the derivatives and their evaluations.
(b) Use the polynomial T₁ (x) that you found in part (a) to write down a sum of terms that gives an
approximation to the value of f(1.3) = (1.3) In(1.3). Give an answer with 6 decimal places.
(c) Use Taylor's Inequality to find an upper bound on the error |R₂(x)] when T₁(x) is used to
approximate ƒ(1.3) = (1.3) In(1.3). Part of your work will be to find a suitable value for "M."
Give an answer with 6 decimal places.
(d) Use a calculator to estimate the value of ƒ(1.3) = (1.3) · In(1.3) to 6 decimal places, and find the
actual error [R₂(x)| resulting from using your estimate in part (b). How does this actual error compare to
the upper bound on the error that you found in part (c)? Explain.
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