Problem 4. For a bounded function f : [a, b] → R and a partition P = {c;}"-1 of [a, b], define %3D n-1 U°(f, P) := sup i=1 *E[xi,&i+1) f(x)(xi+1 – xi) and | n-1 L°(f, P) := E f(x)(xi+1 – x;). inf i=1 Suppose that for a bounded function f: [a, b] → R and a partition P of [a, b], that U°(f, P) = L°(f, P). Provide a characterization of f. %3D
Problem 4. For a bounded function f : [a, b] → R and a partition P = {c;}"-1 of [a, b], define %3D n-1 U°(f, P) := sup i=1 *E[xi,&i+1) f(x)(xi+1 – xi) and | n-1 L°(f, P) := E f(x)(xi+1 – x;). inf i=1 Suppose that for a bounded function f: [a, b] → R and a partition P of [a, b], that U°(f, P) = L°(f, P). Provide a characterization of f. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Problem 4.
For a bounded function f : [a, b] → R and a partition P =
{r;}=1 of [a, b], define
n-1
U°(f, P) := sup
i=1 *E[ri,xi+1)
f(x)(xi+1 – x;) and
n-1
L°(f, P) := E.
inf
f(x)(xi+1 – ¤;).
i=1
Suppose that for a bounded function f: [a, b] → R and a partition P of [a, b], that U°(f,P) =
L°(f, P). Provide a characterization of f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d4bcd37-5435-406e-9dcc-959e9ecc5bc8%2Fb49dad5c-30cd-4e66-86da-b9e2f756e030%2Ffnbyk2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 4.
For a bounded function f : [a, b] → R and a partition P =
{r;}=1 of [a, b], define
n-1
U°(f, P) := sup
i=1 *E[ri,xi+1)
f(x)(xi+1 – x;) and
n-1
L°(f, P) := E.
inf
f(x)(xi+1 – ¤;).
i=1
Suppose that for a bounded function f: [a, b] → R and a partition P of [a, b], that U°(f,P) =
L°(f, P). Provide a characterization of f.
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