Let f: [a, b] → R be a bounded function, and let P = {xo,...,n} be a partition of [a, b]. We say a set of points 7:= {C₁,..., Cn} is a tagging of P if x₁-1 ≤ i ≤ xi for all i = 1,..., n. Given any partition P and tagging r of P, show that 71 L(P, f) ≤ f(c₂) Ax¡ ≤U(P, f) i=1 Suppose f: [a, b] →→ R is Riemann integrable. Show that for all e > 0, there exists a partition P such that for any tagging 7, n f-f(c)Ax;
Let f: [a, b] → R be a bounded function, and let P = {xo,...,n} be a partition of [a, b]. We say a set of points 7:= {C₁,..., Cn} is a tagging of P if x₁-1 ≤ i ≤ xi for all i = 1,..., n. Given any partition P and tagging r of P, show that 71 L(P, f) ≤ f(c₂) Ax¡ ≤U(P, f) i=1 Suppose f: [a, b] →→ R is Riemann integrable. Show that for all e > 0, there exists a partition P such that for any tagging 7, n f-f(c)Ax;
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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