(a) Compute the sixth Maclaurin polynomial T6 for f (x) = sin(x2) by substituting x2 in

Chapter 8, Problem 69

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(a) Compute the sixth Maclaurin polynomial T6 for f (x) = sin(x2) by substituting x2 in P (x) = x x3/6, the third Maclaurin polynomial for f (x) = sin x. (b) Show that |sin(x2) T6(x)| |x| 10 5! . Hint: Substitute x2 for x in the error bound for |sin x P (x)|, noting that P is also the fourth Maclaurin polynomial for f (x) = sin x. (c) Use T6 to approximate 1/2 0 sin(x2)dx and find a bound for the error.

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