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Let f : [0, 00) → R be a monotone function. Prove that lim f(x) = L for some number L if and only if ƒ is bounded. (When we say that ƒ is bounded, we mean that the image f([0, 00)) is a bounded set.)

Let f : [0, 00) → R be a monotone function. Prove that lim f(x) = L for some number L if and only if ƒ is bounded. (When we say that ƒ is bounded, we mean that the image f([0, 00)) is a bounded set.)

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 f : [0, 00) → R be a monotone function. Prove that lim f(x) = L for some number L if and only if ƒ is bounded. (When we say that ƒ is bounded, we mean that the image f([0, 00)) is a bounded set.)
Transcribed Image Text:Let f : [0, 00) → R be a monotone function. Prove that lim f(x) = L for some number L if and only if ƒ is bounded. (When we say that ƒ is bounded, we mean that the image f([0, 00)) is a bounded set.)
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