2. Use the Maclaurin Series to approximate the function f(x) = (x – 2)* using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures. Approximation Step size, h Truncation Error, E Order Maclaurin Series O(h) 0.5 O(h²) 0.5 O(h³) 0.5 O(h*) 0.5 O(h) 5 O(h?) 5 O(h³) What can you conclude about the relationship between the approximation order, step size, and truncation error? Are higher-order approximation orders always better?
2. Use the Maclaurin Series to approximate the function f(x) = (x – 2)* using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures. Approximation Step size, h Truncation Error, E Order Maclaurin Series O(h) 0.5 O(h²) 0.5 O(h³) 0.5 O(h*) 0.5 O(h) 5 O(h?) 5 O(h³) What can you conclude about the relationship between the approximation order, step size, and truncation error? Are higher-order approximation orders always better?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the Maclaurin Series to approximate the function ?(?) = (? − 2)^4 using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures.
Transcribed Image Text:2. Use the Maclaurin Series to approximate the function f (x) = (x – 2)* using each of the
combinations of approximation order and step size. For each approximation, calculate the relative
truncation error to three significant figures.
Approximation
Order
Step size, h
Truncation Error, E
Maclaurin Series
O(h)
0.5
O(h?)
0.5
O(h³)
0.5
O(h*)
0.5
O(h)
5
(G4)0
O(h³)
5
What can you conclude about the relationship between the approximation order, step size, and
truncation error? Are higher-order approximation orders always better?
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