"(a) Let f be the real function on the interval [0, 1] given by f(x) = 0, when x = IT: = 0 when 0 < x≤ 1. Show that for every e > 0 there exists a partition Psuch that U(f, P) - L(f, Pc) < £, where U (f, Pr) and L(f, P.) are the upper and lower Riemann sums for the partition. Use this to determine if f is Riemann integrable."

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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"(a) Let f be the real function on the interval [0, 1] given by
f(x) =
0, when x =
IT:
= 0
when 0 < x≤ 1.
Show that for every e > 0 there exists a partition Psuch that
U(f, P) - L(f, Pc) < £,
where U (f, Pr) and L(f, P.) are the upper and lower Riemann sums for the partition. Use this
to determine if f is Riemann integrable."
Transcribed Image Text:"(a) Let f be the real function on the interval [0, 1] given by f(x) = 0, when x = IT: = 0 when 0 < x≤ 1. Show that for every e > 0 there exists a partition Psuch that U(f, P) - L(f, Pc) < £, where U (f, Pr) 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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