Use a second degree Taylor polynomial to approximate the two solutions to cos(x) = 3/4 in the interval (-"/2, "/2).
Use a second degree Taylor polynomial to approximate the two solutions to cos(x) = 3/4 in the interval (-"/2, "/2).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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Taylor Polynomials! I would appreciate any assistance! The more explanation the better.
Expert Solution
Step 1
Given that,
The function
We want to find two solutions of using second-degree Taylor polynomial
Take
We need to find Taylor's polynomial at x =0.
The Taylor series approximation is given by formula,
Step 2
f'(0) =-sin(0) =0
Thus the second-degree Taylors approximation is,
Step by step
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