Question

Question involving Simpon's rule, Midpoint rule, and the error bound rule. How do I solve for b), d), and g)?

Let f(x)-ecos(x) and 1 -Ís2π f(x) dx (a) Use M1o to approximate I to six decimal places. M17.95492651755339 (b) Use the fact that |f"(x)| e on [0, 2T to obtain an upper bound on the absolute error EM of the approximation from (a). Make sure your answer is correct to six decimal places EM0.16234848503 (c) Use Si0 to approximate I to six decimal places. S10 -7.95378942226367 (d) Use the fact that l f(4)(z)| 〈 4e on [O, 2π] to obtain an upper bound on the absolute error |Esl of the approximation from (c). Make sure your answer is correct to six decimal places (e) Use a CAS to approximate I to six decimal places. 7.954926 (e) Use a CAS to approximate I to six decimal places 7.954926 (f) Which of the two approximations Mio and Sio is better? A. Both are equally good approximations. . V10 C. S10 (g) Using the information given in part (d) and the appropriate error formula from your textbook, how large do we have to choose n to ensure that the approximation Sn is accurate to within o.oo01? (Your answer must be a whole number.) n- O Preview Answer(s)

Answer 1

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