Let f(x) costtx. Use Eq. (4.9) and the values of /(x) at x = 0.25, 0.5, and 0.75 to

Chapter 4, Problem 19

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Let f(x) costtx. Use Eq. (4.9) and the values of /(x) at x = 0.25, 0.5, and 0.75 to approximate /"(0.5). Compare this result to the exact value and to the approximation found in Exercise 15 of Section 3.5. Explain why this method is particularly accurate for this problem and find a bound for the error.

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