Let p 1 and q 1 be the first-order Taylor polynomials for f(x) = x centered at

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Let p1 and q1 be the first-order Taylor polynomials for f(x) = √x centered at 36 and 49, respectively.

a. Find p1 and q1.

b. Complete the following table showing the errors when using p1 and q1 to approximate f(x) at x = 37, 39, 41, 43, 45, and 47. Use a calculator to obtain an exact value of f(x).

|V – p,(x)| |Vx – q1(x)| х 37 39 41 43 45 47

c. At which points in the table is p1 a better approximation to f than q1? Explain this result.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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