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Do the following with the given information. [² 17 17 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = 15.339658 Mg = 15.395539 (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 ≤ 0372537 IEMI ≤ 0186272 nz nz X X (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.) for Tn for Mn

Do the following with the given information. [² 17 17 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = 15.339658 Mg = 15.395539 (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 ≤ 0372537 IEMI ≤ 0186272 nz nz X X (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.) for Tn for Mn

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 14E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...
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Hello, I am not too sure about finding error bounds for integral approximation or how to find n to obtain and an accurate approixmation within an error of .0001.

Do the following with the given information. 1 S 17 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 M8 = 15.339658 (b) Estimate the errors in the approximations Tg and Må 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.) 8 |ET| ≤ .0372537 IEMI ≤ .0186272 nz = 15.395539 n z (c) How large do we have to choose n so that the approximations T and Mn 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.) X X for T for Mn
Transcribed Image Text:Do the following with the given information. 1 S 17 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 M8 = 15.339658 (b) Estimate the errors in the approximations Tg and Må 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.) 8 |ET| ≤ .0372537 IEMI ≤ .0186272 nz = 15.395539 n z (c) How large do we have to choose n so that the approximations T and Mn 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.) X X for T for Mn
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Do the following with the given information. 1 [²₁ 17 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 M8 = 15.339658 15.395539 = (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.) |ET| ≤ .0851080 IEMI ≤ 0425540 X (c) How large do we have to choose n so that the approximations 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 n n ≥ 233 n ≥ 166 X X for Tn for M
Transcribed Image Text:Do the following with the given information. 1 [²₁ 17 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 M8 = 15.339658 15.395539 = (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.) |ET| ≤ .0851080 IEMI ≤ 0425540 X (c) How large do we have to choose n so that the approximations 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 n n ≥ 233 n ≥ 166 X X for Tn for M
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