Do the following with the given information. ²2 23 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) Tg = Mg = (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| ≤ IEMI S (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.) nz n 2 for To for Mn

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time
Section: Chapter Questions
Problem 41A: Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN A slot 812.00...
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please answer part a, b and c

Do the following with the given information.
'1
S 23 cos(x²) dx
(a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.)
8
T8
M8
=
=
(b) Estimate the errors in the approximations T. 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.)
|ET| ≤
IEMI ≤
nz
n
(c) How large do we have to choose n so that the approximations T₁ 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.)
nz
for Tn
for Mn
Transcribed Image Text:Do the following with the given information. '1 S 23 cos(x²) dx (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) 8 T8 M8 = = (b) Estimate the errors in the approximations T. 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.) |ET| ≤ IEMI ≤ nz n (c) How large do we have to choose n so that the approximations T₁ 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.) nz for Tn for Mn
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