The following is a fourth degree (n = 4) Taylor polynomial approximation to some function f(x). f(x) - (x + 1) – (x + 1)² (x + 1)³ + (x + 1)4 4 -1.06 to at least three significant digits. Justify your confidence in the number of correct significant digits in your approximation. Determine the true value of the function at x = –
The following is a fourth degree (n = 4) Taylor polynomial approximation to some function f(x). f(x) - (x + 1) – (x + 1)² (x + 1)³ + (x + 1)4 4 -1.06 to at least three significant digits. Justify your confidence in the number of correct significant digits in your approximation. Determine the true value of the function at x = –
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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Transcribed Image Text:The following is a fourth degree (n = 4) Taylor polynomial approximation to some function
f(r).
(x +1)² , (x +1)³ (x+1)*
(x+ 1)3
(x + 1)4
f (x) 2 (x+ 1) –
3
4
Determine the true value of the function at x = -1.06 to at least three significant digits.
Justify your confidence in the number of correct significant digits in your approximation.
Transcribed Image Text:HINTS: You do not know the true value so you must use the approximate relative error
somehow to determine the number of significant digits. To use the approximate relative error
you need to iteratively approxiamte the function at x = -1.06, i.e. calculate a po, then a P1,
etc. until you have a good approximation.
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