(b) Explain why U(f, P') – L(f, P') < e/3. By the previous exercise, if we can show U(f, P) < U(f, P') + €/3 (and similarly L(f, P') – €/3|< L(f, P)), then it will follow that R(f, P)- f< €

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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Explain why both the Riemann sum R(f,P) and )f b/a f
fall between L(f,P) and U(f,P). (b) Explain why U(f,P1) − L(f,P1) < /3. By the previous exercise, if we can show U(f,P) < U(f,P) + /3 (and
similarly L(f,P) − /3 < L(f,P)), then it will follow that and the proof will be done. Thus, we turn our attention toward estimating the
distance between U(f,P) and U(f,P).

(b) Explain why U(f, P') – L(f, P') < e/3.
By the previous exercise, if we can show U(f, P) < U(f, P') + €/3 (and
similarly L(f, P') – €/3|< L(f, P)), then it will follow that
R(f, P)-
f< €
Transcribed Image Text:(b) Explain why U(f, P') – L(f, P') < e/3. By the previous exercise, if we can show U(f, P) < U(f, P') + €/3 (and similarly L(f, P') – €/3|< L(f, P)), then it will follow that R(f, P)- f< €
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