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Let I (a, b) be a bounded open interval and ƒ : I → be a monotone increasing function on I. (i) If f is bounded above on I, then lim f(x) sup f(x). x€(a,b) x46-

Let I (a, b) be a bounded open interval and ƒ : I → be a monotone increasing function on I. (i) If f is bounded above on I, then lim f(x) sup f(x). x€(a,b) x46-

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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Let I = (a, b) be a bounded open interval and f:I → R be a monotone increasing function on I. (i) If fƒ is bounded above on I, then lim f(x) sup f(x). x = (a,b) x→6- (ii) If ƒ is bounded below on I, then lim f(x)= inf f(x). ze(a,b) x→a+ to ∞. (iii) If ƒ is unbounded above on I, then lim f(x) (iv) If ƒ is unbounded below on I, then lim f(x) x→b- xat -∞o.
Transcribed Image Text:Let I = (a, b) be a bounded open interval and f:I → R be a monotone increasing function on I. (i) If fƒ is bounded above on I, then lim f(x) sup f(x). x = (a,b) x→6- (ii) If ƒ is bounded below on I, then lim f(x)= inf f(x). ze(a,b) x→a+ to ∞. (iii) If ƒ is unbounded above on I, then lim f(x) (iv) If ƒ is unbounded below on I, then lim f(x) x→b- xat -∞o.
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