4. Let f(x) = exp{sin(x)} = esin(x). The Taylor polynomial of degree 6 centered at 0 for f(x) is P6(x) = 1 + x + x² 2 8

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4 Let F X Exp Sin X Esin X The Taylor Polynomial Of Degree 6 Centered At 0 For F X Is P6 X 1 X X 2 8 1 (62.54 KiB) Viewed 39 times

4. Let f(x) = exp{sin(x)} = esin(x). The Taylor polynomial of degree 6 centered at 0 for f(x) is P6(x) = 1 + x + x² 2 8 max −1/2≤x≤1/2 x5 15 240 x6 (a) Given that f(7)(x)| < 120 for |x| <, estimate the error in approximating f(x) by the Taylor polynomial on the interval [—½, ½]: |ƒ(x) − P6(x)| ≤__ ?? (b) Compute p6(1/2). (c) Compute f(1/2) and compare it with the estimate in part (b). How does the actual error compare with the estimate of the error obtained in part (a)?