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Consider an integrable function f and a rectangle R which is a subset of its domain. Only one of the following statements is always TRUE. Which one? There exists a partition P of R such that Lp (f) = IR(f). For all partitions P of Rwe have Lp (f) #IR(f). ○ If Lp (f) = Up (f) for some partition P of R, then IR (f) = IR (f). O For any partition P of R we have Lp (f) = Up(f). For any partition P of Rwe have Lp (f) ‡ Up(f).

Consider an integrable function f and a rectangle R which is a subset of its domain. Only one of the following statements is always TRUE. Which one? There exists a partition P of R such that Lp (f) = IR(f). For all partitions P of Rwe have Lp (f) #IR(f). ○ If Lp (f) = Up (f) for some partition P of R, then IR (f) = IR (f). O For any partition P of R we have Lp (f) = Up(f). For any partition P of Rwe have Lp (f) ‡ Up(f).

Advanced Engineering Mathematics
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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Consider an integrable function f and a rectangle R which is a subset of its domain. Only one of the following statements is always TRUE. Which one? There exists a partition P of R such that Lp (f) = IR(f). For all partitions P of Rwe have Lp (f) #IR(f). ○ If Lp (f) = Up (f) for some partition P of R, then IR (f) = IR (f). For any partition P of R we have Lp (f) = Up(f). O For any partition Pof R we have Lp (f) ‡ Up(f).
Transcribed Image Text:Consider an integrable function f and a rectangle R which is a subset of its domain. Only one of the following statements is always TRUE. Which one? There exists a partition P of R such that Lp (f) = IR(f). For all partitions P of Rwe have Lp (f) #IR(f). ○ If Lp (f) = Up (f) for some partition P of R, then IR (f) = IR (f). For any partition P of R we have Lp (f) = Up(f). O For any partition Pof R we have Lp (f) ‡ Up(f).
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