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n logn² e Q (n), for any integer constant k > 0.

n logn² e Q (n), for any integer constant k > 0.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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## Problem Statement ### Task: Prove that the following statements are true (T) or false (F). (Let \( \log n = \log_2 n \)). You must define first what you are trying to prove using the limit definition. ### Statements: a) \( \frac{n^3}{\log n} \in O(n^k) \), for any integer constant \( 2 \leq k \leq 3 \). b) \( n + n \log n^k \in \Theta(n \log n) \), for any positive integer constant \( k \). c) \( n \log n^2 \in \Omega(n^{k_\omega}) \), for any integer constant \( k > 0 \).
Transcribed Image Text:## Problem Statement ### Task: Prove that the following statements are true (T) or false (F). (Let \( \log n = \log_2 n \)). You must define first what you are trying to prove using the limit definition. ### Statements: a) \( \frac{n^3}{\log n} \in O(n^k) \), for any integer constant \( 2 \leq k \leq 3 \). b) \( n + n \log n^k \in \Theta(n \log n) \), for any positive integer constant \( k \). c) \( n \log n^2 \in \Omega(n^{k_\omega}) \), for any integer constant \( k > 0 \).
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