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Let f(x)= sin x where x is in radian and |x| ≤/2. Using the Tailor series expansion about xo = 0, find the polynomial approximation Pn(x) of the smallest degree n such that this approximation has the error bound f(x) - Pn(x)| ≤ 10-10 for all |x| ≤π/2.

Let f(x)= sin x where x is in radian and |x| ≤/2. Using the Tailor series expansion about xo = 0, find the polynomial approximation Pn(x) of the smallest degree n such that this approximation has the error bound f(x) - Pn(x)| ≤ 10-10 for all |x| ≤π/2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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Let f(x) = sinx where x is in radian and [x] ≤ π/2. Using the Tailor series expansion about x = 0, find the polynomial approximation Pn(x) of the smallest degree n such that this approximation has the error bound |ƒ(x) − Pn(x)| ≤ 10-¹⁰ for all |x| ≤ π/2.
Transcribed Image Text:Let f(x) = sinx where x is in radian and [x] ≤ π/2. Using the Tailor series expansion about x = 0, find the polynomial approximation Pn(x) of the smallest degree n such that this approximation has the error bound |ƒ(x) − Pn(x)| ≤ 10-¹⁰ for all |x| ≤ π/2.
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