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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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