Let f(x) = ln x and let p n and q n be the nthorder Taylor polynomials

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Let f(x) = ln x and let pn and qn be the nthorder Taylor polynomials for f centered at 1 and e, respectively. 

a. Find p3 and q3.

b. Graph f, p3, and qon the interval [0, 4].

c. Complete the following table showing the errors in the approximations given by p3 and q3 at selected points.

|In x – p:(x)|| |In x - 43(x)| х 0.5 1.0 1.5 2.5 3 3.5

d. At which points in the table is p3 a better approximation to f than q3? Explain your observations.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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