Question: (a) Use the Maclaurin polynomials P 1 (x), P 3 (x), and P 5 (x) for f(x) = sin x to complete the table. (b)

(a) Use the Maclaurin polynomials P₁(x), P₃(x), and P₅(x) for f(x) = sin x to complete the table.

X sin x P(x) P3(x) P;(x) 0 0.25 0 0.2474 0.50 0.4794

(b) Use a graphing utility to graph f(x) = sin x and the Maclaurin polynomials in part (a).(c) Describe the change in accuracy of a polynomial approximation as the distance from the point where the polynomial is centered increases.

X sin x P(x) P3(x) P;(x) 0 0.25 0 0.2474 0.50 0.4794 0.6816 0.75 1 0.8415

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