Let T4 be the fourth Maclaurin polynomial for f (x) = cos x. (a) Show that

Chapter 8, Problem 67

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Let T4 be the fourth Maclaurin polynomial for f (x) = cos x. (a) Show that | cos x T4(x)| 1 2 6 6! for all x 0, 1 2 Hint: T4(x) = T5(x). (b) Evaluate 1/2 0 T4(x) dx as an approximation to 1/2 0 cos x dx. Use Exercise 66 to find a bound for the size of the error.

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