6) Consider the function 1- cos(3x) S(x) =: 9x a) Explain why this way of computing the function (x) is problematic if x is near certain values. What are these problematic values? b) Use the trigonometric identity, sin' u =-cOs(20) to obtain another form of f(x) less 2 prone to error. Find an annnorimat to grror hy finding the
6) Consider the function 1- cos(3x) S(x) =: 9x a) Explain why this way of computing the function (x) is problematic if x is near certain values. What are these problematic values? b) Use the trigonometric identity, sin' u =-cOs(20) to obtain another form of f(x) less 2 prone to error. Find an annnorimat to grror hy finding the
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:6) Consider the function
S(x) =-cos(3.x)
9x
a) Explain why this way of computing the function (x) is problematic if x is near certain
values. What are these problematic values?
b) Use the trigonometric identity, sin’ u =
1-cos(2u)
- to obtain another form of f(x) less
2
prone to error.
c) Find an approximation for f(x), called g(x), that is less prone to error by finding the
first 3 nonzero terms of a power series for (x), using the Maclaurin series,
cos.r = 5-1)*x*
= (2k)!
(Recall that a Maclaurin series is a Taylor series centered at 0.)
d) Compute lim- cos(3x)
9x
using L'Hôpital's rule on this original form of the function.
Then, compute lim g(x) (the approximation you found in part (c)), and compare your
results.
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