Given. 1 6.² Do the following. (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = Mg 13 cos(x²) dx = (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| S IEMI S (c) How large do we have to choose n so that the approximations T₁ 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.) nz ΠΣ for Tn for Mn
Given. 1 6.² Do the following. (a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.) T8 = Mg 13 cos(x²) dx = (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| S IEMI S (c) How large do we have to choose n so that the approximations T₁ 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.) nz ΠΣ for Tn for Mn
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Given.
1
6.²
Do the following.
(a) Find the approximations Tg and Mg for the given integral. (Round your answer to six decimal places.)
T8 =
Mg
13 cos(x²) dx
=
(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| S
IEMI S
(c) How large do we have to choose n so that the approximations T₁ 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.)
nz
ΠΣ
for Tn
for Mn
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