The Maclaurin series expansion for sin x is: sin x = x - x³ x5 x7 x⁹ + 5! 7! 9! 3! Use this expansion to find the answers to the following: 5. Find the true error and true relative error when the first 3 terms of the given series are used to estimate sin(1/6). Give your answers to 4 significant digits. 6. Find the absolute approximate error and relative absolute approximate error when the first 2 and first 3 nonzero terms are used to estimate sin(x/6). Give your answers to 3 significant digits.
The Maclaurin series expansion for sin x is: sin x = x - x³ x5 x7 x⁹ + 5! 7! 9! 3! Use this expansion to find the answers to the following: 5. Find the true error and true relative error when the first 3 terms of the given series are used to estimate sin(1/6). Give your answers to 4 significant digits. 6. Find the absolute approximate error and relative absolute approximate error when the first 2 and first 3 nonzero terms are used to estimate sin(x/6). Give your answers to 3 significant digits.
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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Please do exercise 5 and 6 and please show work
Transcribed Image Text:The Maclaurin series expansion for sin x is:
sin x = x-
+
3! 5! 7! 9!
Use this expansion to find the answers to the following:
5. Find the true error and true relative error when the first 3 terms of the given series are used to
estimate sin(7/6). Give your answers to 4 significant digits.
6.
Find the absolute approximate error and relative absolute approximate error when the first 2 and
first 3 nonzero terms are used to estimate sin(1/6). Give your answers to 3 significant digits.
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