Let f(x) = sin x and let p n and q n be nth order Taylor polynomials

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Let f(x) = sin x and let pn and qn be nth order Taylor polynomials for f centered at 0 and π, respectively. 

a. Find p5 and q5.

b. Graph f, p5, and q5 on the interval [-π, 2π]. On what interval is p5 a better approximation to f than q5? On what interval is q5 a better approximation to f than p5

c. Complete the following table showing the errors in the approximations given by pand q5 at selected points.

|sin x – ps(x)| |sin x – 45 (x)| х TT/4 T/2 Зп /4 5/4 7п /4

d. At which points in the table is p5 a better approximation to f than q5? At which points do p5 and q5 give comparable approximations to f ? Explain your observations.

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Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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