(a) Let ƒ be the real function on the interval [0, 1] given by f(x)= [0, when z=0 when 0 <=<1. Show that for every e > 0 there exists a partition P, such that U(ƒ, P.) — L(ƒ, P.)
(a) Let ƒ be the real function on the interval [0, 1] given by f(x)= [0, when z=0 when 0 <=<1. Show that for every e > 0 there exists a partition P, such that U(ƒ, P.) — L(ƒ, P.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(a) Let f be the real function on the interval [0, 1] given by
f(x)=
0,
,
when z = 0
when 0 <z≤1.
Show that for every e > 0 there exists a partition P, such that
U(f, P.) - L(f, P.) < e,
where U (f, P.) and L(f, P.) are the upper and lower Riemann sums for the partition. Use this
to determine if f is Riemann integrable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8070592d-4a31-42d2-bef1-b46c168ad043%2Fa0c570f9-a3a3-4460-9f82-d3f9a702ecd5%2Ftaj0odr_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let f be the real function on the interval [0, 1] given by
f(x)=
0,
,
when z = 0
when 0 <z≤1.
Show that for every e > 0 there exists a partition P, such that
U(f, P.) - L(f, P.) < e,
where U (f, P.) and L(f, P.) are the upper and lower Riemann sums for the partition. Use this
to determine if f is Riemann integrable.
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