Mathematics

Mathematics

Problem

Let P2(x)P_2(x), P4(x)P_4(x), and P6(x)P_6(x) denote the degree 22, 44, and 66 Maclaurin polynomials for sin⁡x\sin x, respectively. Which of the following lists these polynomials in order of increasing absolute error when they are used to approximate sin⁡(0.5)\sin(0.5)? a) P2,  P4,  P6P_2,\;P_4,\;P_6 b) P4,  P6,  P2P_4,\;P_6,\;P_2 c) P6,  P4,  P2P_6,\;P_4,\;P_2 d) P4,  P2,  P6P_4,\;P_2,\;P_6

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