Do the following with the given information. 9 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) Тв Ma == 8.120998 = (b) Estimate the errors in the approximations Tg and Mg in part (a). (Use the fact that the range of the sine and cosine functions is bounded by +1 to estimate the maximum error. Round your answer to seven decimal places.) |E| S IEMI ≤ (c) How large do we have to choose n so that the approximations T and M to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error.) n≥ 213 n≥ 150 for Tn for M n n n 1 Draw the graph of f(x) = sin x2 in the viewing rectangle [0, 1] by [0, 0.5] and let I = (a) Use the graph to decide whether L2, R2, M2, and T2 underestimate or overestimate I. O42 will underestimate I. O 42 will overestimate I. f(x) dx. R2 will underestimate I. R2 will overestimate I. OM2 will underestimate I. OM2 will overestimate I. Ο Τ2 Ο Τ2 will underestimate I. will overestimate I. (b) For any value of n, list the numbers L, R MT and I in increasing order. (Enter your answers as a comma-separated list.) Ln, Rn,I,Mn, Tn (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) L5 R5 0.0579 = 0.1879 × × M5 = 0.1099 × T5 = 0.1229 × From the graph, which do you think gives the best estimate of I? Լո Rn ○ Mn ○ Tn
Do the following with the given information. 9 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) Тв Ma == 8.120998 = (b) Estimate the errors in the approximations Tg and Mg in part (a). (Use the fact that the range of the sine and cosine functions is bounded by +1 to estimate the maximum error. Round your answer to seven decimal places.) |E| S IEMI ≤ (c) How large do we have to choose n so that the approximations T and M to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error.) n≥ 213 n≥ 150 for Tn for M n n n 1 Draw the graph of f(x) = sin x2 in the viewing rectangle [0, 1] by [0, 0.5] and let I = (a) Use the graph to decide whether L2, R2, M2, and T2 underestimate or overestimate I. O42 will underestimate I. O 42 will overestimate I. f(x) dx. R2 will underestimate I. R2 will overestimate I. OM2 will underestimate I. OM2 will overestimate I. Ο Τ2 Ο Τ2 will underestimate I. will overestimate I. (b) For any value of n, list the numbers L, R MT and I in increasing order. (Enter your answers as a comma-separated list.) Ln, Rn,I,Mn, Tn (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) L5 R5 0.0579 = 0.1879 × × M5 = 0.1099 × T5 = 0.1229 × From the graph, which do you think gives the best estimate of I? Լո Rn ○ Mn ○ Tn
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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