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(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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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(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?
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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