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
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F199f5825-34df-447d-9f09-7002fbf61b35%2Fe4f64734-c25b-4ab2-9c06-4cd216485a48%2Fa1e4bh_processed.png&w=3840&q=75)
Transcribed Image Text: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
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