Find the second Taylor polynomial P₂(x) for the function f(x) = e cos x about x₁ = π/3 a. Use P₂ (0.5) to approximate f (0.5). Find an upper bound for error | f (0.5) - P₂ (0.5)| using the error formula, and compare it to the actual error. b. Find a bound for the error f(x) - P₂(x)| in using P2(x) to approximate f(x) on the interval [0, 1]. Approximate f f(x) dx using P₂(x) dx. C.
Find the second Taylor polynomial P₂(x) for the function f(x) = e cos x about x₁ = π/3 a. Use P₂ (0.5) to approximate f (0.5). Find an upper bound for error | f (0.5) - P₂ (0.5)| using the error formula, and compare it to the actual error. b. Find a bound for the error f(x) - P₂(x)| in using P2(x) to approximate f(x) on the interval [0, 1]. Approximate f f(x) dx using P₂(x) dx. C.
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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![Find the second Taylor polynomial P₂(x) for the function f(x) = e cos x about x₁ = π/3
a. Use P₂ (0.5) to approximate f (0.5). Find an upper bound for error | f (0.5) - P₂ (0.5)| using the
error formula, and compare it to the actual error.
b. Find a bound for the error f(x) - P₂(x)| in using P2(x) to approximate f(x) on the interval
[0, 1].
Approximate ff(x) dx using
P₂(x) dx.
C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d6b17d3-c01a-4e38-a03d-ada41aa253db%2F3e76d2ab-0f16-4575-a912-f5a6ef0cbb93%2F7kn5hn_processed.png&w=3840&q=75)
Transcribed Image Text:Find the second Taylor polynomial P₂(x) for the function f(x) = e cos x about x₁ = π/3
a. Use P₂ (0.5) to approximate f (0.5). Find an upper bound for error | f (0.5) - P₂ (0.5)| using the
error formula, and compare it to the actual error.
b. Find a bound for the error f(x) - P₂(x)| in using P2(x) to approximate f(x) on the interval
[0, 1].
Approximate ff(x) dx using
P₂(x) dx.
C.
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