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Do the following with the given information. L 1 S² 9 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = 8.120998 M8 = 8.101214 ☑ (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.) IET 0.0015252 × EMI 0.0007626 (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 Mn Draw the graph of f(x) = sin x² in the viewing rectangle [0, 1] by [0, 0.5] and let I = 2 -L'Ax f(x) dx. (a) Use the graph to decide whether L2, R2, M2, and T2 underestimate or overestimate I. 42 will underestimate I. 42 will overestimate I. R2 will underestimate I. R2 will overestimate I. M2 will underestimate I. M2 will overestimate I. T2 will underestimate I. T2 will overestimate I. (b) For any value of n, list the numbers Ln, RM Ln, Mn,J, Tn,Rn n' T and I in increasing order. (Enter your answers as a comma-separated list.) (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) = 0.1187 45 R5 = 0.2146 Ms = |0.1618 T5 = 0.1666 From the graph, which do you think gives the best estimate of I? Rn Mn T n

Do the following with the given information. L 1 S² 9 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = 8.120998 M8 = 8.101214 ☑ (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.) IET 0.0015252 × EMI 0.0007626 (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 Mn Draw the graph of f(x) = sin x² in the viewing rectangle [0, 1] by [0, 0.5] and let I = 2 -L'Ax f(x) dx. (a) Use the graph to decide whether L2, R2, M2, and T2 underestimate or overestimate I. 42 will underestimate I. 42 will overestimate I. R2 will underestimate I. R2 will overestimate I. M2 will underestimate I. M2 will overestimate I. T2 will underestimate I. T2 will overestimate I. (b) For any value of n, list the numbers Ln, RM Ln, Mn,J, Tn,Rn n' T and I in increasing order. (Enter your answers as a comma-separated list.) (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) = 0.1187 45 R5 = 0.2146 Ms = |0.1618 T5 = 0.1666 From the graph, which do you think gives the best estimate of I? Rn Mn T n

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Do the following with the given information. L 1 S² 9 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = 8.120998 M8 = 8.101214 ☑ (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.) IET 0.0015252 × EMI 0.0007626 (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 Mn
Transcribed Image Text:Do the following with the given information. L 1 S² 9 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = 8.120998 M8 = 8.101214 ☑ (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.) IET 0.0015252 × EMI 0.0007626 (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 Mn
Draw the graph of f(x) = sin x² in the viewing rectangle [0, 1] by [0, 0.5] and let I = 2 -L'Ax f(x) dx. (a) Use the graph to decide whether L2, R2, M2, and T2 underestimate or overestimate I. 42 will underestimate I. 42 will overestimate I. R2 will underestimate I. R2 will overestimate I. M2 will underestimate I. M2 will overestimate I. T2 will underestimate I. T2 will overestimate I. (b) For any value of n, list the numbers Ln, RM Ln, Mn,J, Tn,Rn n' T and I in increasing order. (Enter your answers as a comma-separated list.) (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) = 0.1187 45 R5 = 0.2146 Ms = |0.1618 T5 = 0.1666 From the graph, which do you think gives the best estimate of I? Rn Mn T n
Transcribed Image Text:Draw the graph of f(x) = sin x² in the viewing rectangle [0, 1] by [0, 0.5] and let I = 2 -L'Ax f(x) dx. (a) Use the graph to decide whether L2, R2, M2, and T2 underestimate or overestimate I. 42 will underestimate I. 42 will overestimate I. R2 will underestimate I. R2 will overestimate I. M2 will underestimate I. M2 will overestimate I. T2 will underestimate I. T2 will overestimate I. (b) For any value of n, list the numbers Ln, RM Ln, Mn,J, Tn,Rn n' T and I in increasing order. (Enter your answers as a comma-separated list.) (c) Compute L5, R 5, M5, and T5. (Round your answer to four decimal places.) = 0.1187 45 R5 = 0.2146 Ms = |0.1618 T5 = 0.1666 From the graph, which do you think gives the best estimate of I? Rn Mn T n
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