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2.23. Consider f: R→ R. Let S be the set of functions defined by putting g € S if there exist positive constants c, a € R such that g(x)| ≤ c f(x)| for all x > a. Without words of negation, state the meaning of "g & S". (Comment: The set S (written as O(f)) is used to compare the "order of growth" of functions.)

2.23. Consider f: R→ R. Let S be the set of functions defined by putting g € S if there exist positive constants c, a € R such that g(x)| ≤ c f(x)| for all x > a. Without words of negation, state the meaning of "g & S". (Comment: The set S (written as O(f)) is used to compare the "order of growth" of functions.)

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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2.23. Consider \( f: \mathbb{R} \to \mathbb{R} \). Let \( S \) be the set of functions defined by putting \( g \in S \) if there exist positive constants \( c, a \in \mathbb{R} \) such that \( |g(x)| \leq c|f(x)| \) for all \( x > a \). Without words of negation, state the meaning of “\( g \notin S \)”. (Comment: The set \( S \) (written as \( O(f) \)) is used to compare the “order of growth” of functions.)
Transcribed Image Text:2.23. Consider \( f: \mathbb{R} \to \mathbb{R} \). Let \( S \) be the set of functions defined by putting \( g \in S \) if there exist positive constants \( c, a \in \mathbb{R} \) such that \( |g(x)| \leq c|f(x)| \) for all \( x > a \). Without words of negation, state the meaning of “\( g \notin S \)”. (Comment: The set \( S \) (written as \( O(f) \)) is used to compare the “order of growth” of functions.)
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