topic: taylor polinomials source: ISBN 9781319055936 Page: 600-603 In Exercises 71-75, we estimate integrals using Taylor polynomials. Exer- cise 72 is used to estimate the error. 75. (a) Compute the sixth Maclaurin polynomial To for f(x) = sin(x2) by substituting x in P(x) = x - x /6, the third Maclaurin polynomial for f (x) = sinx. (b) Show that | sin(x2) - To(x)| s " 1x1 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) = sinx. 1/2 (c) Use To to approximate sin(x2) dx and find a bound for the error