Mathematics, 21.05.2020 04:08, mikaelalcool1

G (1 point) Let f(x)=4−x3−−−−−√ and I=∫1−1f(x)dx. (a) Use M10 to approximate I to six decimal places. M10= (b) Use the fact that |f′′(x)|≤543–√ on [−1,1] 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. |EM|≤ (c) Use S10 to approximate I to six decimal places. S10= (d) Use the fact that |f(4)(x)|≤167163–√ on [−1,1] to obtain an upper bound on the absolute error |ES| of the approximation from (c). Make sure your answer is correct to six decimal places. |ES|≤ (e) Use a CAS to approximate I to six decimal places. I≈ (f) Which of the two approximations M10 and S10 is better? A. S10 B. M10 C. Both are equally good approximations. (g) Using the information given in part (d) and the appropriate error formula in your textbook, how large do we have to choose n to ensure that the approximation Sn is accurate to within 0.0001? (Your answer must be a whole number.) n =

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G (1 point) Let f(x)=4−x3−−−−−√ and I=∫1−1f(x)dx. (a) Use M10 to approximate I to six decimal places...