1. Let f(r) 3, for each positive integer n, consider the regular partition 0 o x2 < - *. < In-1 < In = 1 of 0, 1] into n many equal-sized subintervals. Denote the corresponding Right-hand Riemann sum by Σία) Δ i=1 (a) For each n, Rn rdx, but what is the smallest value of n for which Rn is within d? (Hint: find a formula for Rn in terms of n) 0.1 of the exact value of (b) If a different choice for rin ri-1, X], for i = 1,2, ... , n is chosen to construct the Riemann sum Σ)Δn i=1 Idr, for a smaller value can the resulting sum be within 0.1 of the exact value of of n than in part (a)? If so, give an example. If not, explain why
1. Let f(r) 3, for each positive integer n, consider the regular partition 0 o x2 < - *. < In-1 < In = 1 of 0, 1] into n many equal-sized subintervals. Denote the corresponding Right-hand Riemann sum by Σία) Δ i=1 (a) For each n, Rn rdx, but what is the smallest value of n for which Rn is within d? (Hint: find a formula for Rn in terms of n) 0.1 of the exact value of (b) If a different choice for rin ri-1, X], for i = 1,2, ... , n is chosen to construct the Riemann sum Σ)Δn i=1 Idr, for a smaller value can the resulting sum be within 0.1 of the exact value of of n than in part (a)? If so, give an example. If not, explain why
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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![1. Let f(r) 3, for each positive integer n, consider the regular partition
0 o
x2 < - *. < In-1 < In = 1
of 0, 1] into n many equal-sized subintervals. Denote the corresponding Right-hand
Riemann sum by
Σία) Δ
i=1
(a) For each n, Rn
rdx, but what is the smallest value of n for which Rn is within
d? (Hint: find a formula for Rn in terms of n)
0.1 of the exact value of
(b) If a different choice for rin ri-1, X], for i = 1,2, ... , n is chosen to construct the
Riemann sum
Σ)Δn
i=1
Idr, for a smaller value
can the resulting sum be within 0.1 of the exact value of
of n than in part (a)? If so, give an example. If not, explain why](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28939ce1-0727-4fe2-bb4f-e0471da7e82d%2F8f62359a-bec9-4abf-8838-8cf0326bbb12%2F89b7x69.png&w=3840&q=75)
Transcribed Image Text:1. Let f(r) 3, for each positive integer n, consider the regular partition
0 o
x2 < - *. < In-1 < In = 1
of 0, 1] into n many equal-sized subintervals. Denote the corresponding Right-hand
Riemann sum by
Σία) Δ
i=1
(a) For each n, Rn
rdx, but what is the smallest value of n for which Rn is within
d? (Hint: find a formula for Rn in terms of n)
0.1 of the exact value of
(b) If a different choice for rin ri-1, X], for i = 1,2, ... , n is chosen to construct the
Riemann sum
Σ)Δn
i=1
Idr, for a smaller value
can the resulting sum be within 0.1 of the exact value of
of n than in part (a)? If so, give an example. If not, explain why
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