3 please 1. State the definition of a Riemann sum and the definition of what it meansfor a function to be Riemann integrable.2. Let S(f, P) denote the upper Darboux sum of f with partition P. Provethat if Qis a refinement of P, then S(f, Q) ≤ S(f, P).3. Let f: [0, 1] →→ R be defined byif x ≤ 1/1/2<{:if x > 1/1.Let > 0. Prove that there exists a partition, P, of [0, 1] withS(f,P)s(f, P) < €.What can you conclude about f?f(x)

The given function is defined as follows.We know that if is a partition of and the function is…

Answered: Let f [0, 1] → R be defined by if x ≤…

Let f [0, 1] → R be defined by if x ≤ 1/2 if x > 1/1. Let € > 0. Prove that there exists a partition, P, of [0, 1] with S(f, P) s(f, P) < €. f(x) -{i = What can you conclude about f?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

3 please

1. State the definition of a Riemann sum and the definition of what it means
for a function to be Riemann integrable.
2. Let S(f, P) denote the upper Darboux sum of f with partition P. Prove
that if Qis a refinement of P, then S(f, Q) ≤ S(f, P).
3. Let f: [0, 1] →→ R be defined by
if x ≤ 1/1/2
<
{:
if x > 1/1.
Let > 0. Prove that there exists a partition, P, of [0, 1] with
S(f,P)
s(f, P) < €.
What can you conclude about f?
f(x)

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