Approximating sin x Let ƒ(x) = sin x, and let pn and qn be nth-order Taylor polynomials for ƒ centered at 0 and p, respectively.a. Find p5 and q5.b. Graph ƒ, p5, and q5 on the interval [-π, 2π]. On what interval is p5 a better approximation to ƒ than q5? On what interval is q5 a better approximation to ƒ than p5?c. Complete the following table showing the errors in the approximations given by p5 and q5 at selected points.d. At which points in the table is p5 a better approximation to ƒ than q5? At which points do p5 and q5 give equal approximations to ƒ? Explain your observations. Isinx - P:(x)| |sinx – q; (x)|п/4п/2Зп /45и/47п/4

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Isinx - P:(x)| |sinx – q; (x)| п/4 п/2 Зп /4 5и/4 7п/4

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 20E

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Question

Approximating sin x Let ƒ(x) = sin x, and let p_n and q_n be nth-order Taylor polynomials for ƒ centered at 0 and p, respectively.
a. Find p₅ and q₅.
b. Graph ƒ, p₅, and q₅ on the interval [-π, 2π]. On what interval is p₅ a better approximation to ƒ than q₅? On what interval is q₅a better approximation to ƒ than p₅?
c. Complete the following table showing the errors in the approximations given by p₅ and q₅ at selected points.
d. At which points in the table is p₅ a better approximation to ƒ than q₅? At which points do p₅ and q₅ give equal approximations to ƒ? Explain your observations.

Isinx - P:(x)| |sinx – q; (x)|
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