Mark all statements that are correct (there might be more than one statement that is correct). 0 b f³fz fº f> f then f is Riemann integrable over [a,b]. Let f:[a, b] →R be bounded. If Let f:[0,1] → R be given by f(x) = x. For every ɛ>0 there is a partition P ={ Σ(M,(f) – m, (f) ) A x,<ɛ. j=1 0 = 1 The function f:[0,1]→R be given by f(x) = X if x=0 if 0

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Mark all statements that are correct (there might be more than one statement that is correct).
b
2 f₁
Let f: [a, b] → R be bounded. If
b
Sºf
n
Σ(Μ.
(M, (f) – m; (f) ) A x,<e.
fz
Let f:[0,1] → R be given by f(x) = x. For every e > 0 there is a partition P = {X₂X₁,...,x} of [0,1], such that
f then f is Riemann integrable over [a, b]
0
HA
1
X
The function f:[0,1]→R be given by f(x) =
if x=0
if 0<x< 1
is Riemann integrable.
Let P be a partition of [a, b] and Q=PU {C}, where c € [a,b], c # P. Then L(f,Q) ≤ L(f,P) and
U(f,P) ≤ U(f, Q).
Let P, Q be partitions of [a,b] and f:[a, b] → R be bounded. Then U(f,P) ≤ L(f,Q).
Transcribed Image Text:Mark all statements that are correct (there might be more than one statement that is correct). b 2 f₁ Let f: [a, b] → R be bounded. If b Sºf n Σ(Μ. (M, (f) – m; (f) ) A x,<e. fz Let f:[0,1] → R be given by f(x) = x. For every e > 0 there is a partition P = {X₂X₁,...,x} of [0,1], such that f then f is Riemann integrable over [a, b] 0 HA 1 X The function f:[0,1]→R be given by f(x) = if x=0 if 0<x< 1 is Riemann integrable. Let P be a partition of [a, b] and Q=PU {C}, where c € [a,b], c # P. Then L(f,Q) ≤ L(f,P) and U(f,P) ≤ U(f, Q). Let P, Q be partitions of [a,b] and f:[a, b] → R be bounded. Then U(f,P) ≤ L(f,Q).
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