(a) Let f(x) = 2 sin x. Write down the Taylor polynomial approximation of degree 2, p2(x), for the function f(x) about the point x0 = 0. Make sure to include the remainder term. (b) How large should n be chosen to have |f(x) - Pn(x)|≤ 10-3 on 0 ≤ x ≤ π/2?
(a) Let f(x) = 2 sin x. Write down the Taylor polynomial approximation of degree 2, p2(x), for the function f(x) about the point x0 = 0. Make sure to include the remainder term. (b) How large should n be chosen to have |f(x) - Pn(x)|≤ 10-3 on 0 ≤ x ≤ π/2?
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:(a) Let f(x) = 2 sin x. Write down the Taylor polynomial approximation of degree 2, p2(x), for the
function f(x) about the point x0 = 0. Make sure to include the remainder term.
(b) How large should n be chosen to have
|f(x) - Pn(x)|≤ 10-3 on 0 ≤ x ≤ π/2?
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