Problem 2 Find the smallest integer p such that f(n) = O(n²) for each of the following choices of the function f. You may assume that n€ N. You should explain your answers but do not need to write formal proofs. You may find it useful to remember that log n ‡ 0(1) and log n ≤ n for all n. 1. f(n) = 3n² 2. f(n) = log n 3. f(n) = n²log n

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
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Problem 2
Find the smallest integer p such that f(n) = O(nº) for each of the following
choices of the function f. You may assume that n E N. You should explain
your answers but do not need to write formal proofs. You may find it useful to
remember that logn & 0(1) and log n ≤ n for all n.
1. f(n) = 3n²
2. f(n) = log n
3. f(n) = n²log n
log n
4. f(n) =
=
5. f(n)
=
n
n³+2
n²_n-1
Transcribed Image Text:Problem 2 Find the smallest integer p such that f(n) = O(nº) for each of the following choices of the function f. You may assume that n E N. You should explain your answers but do not need to write formal proofs. You may find it useful to remember that logn & 0(1) and log n ≤ n for all n. 1. f(n) = 3n² 2. f(n) = log n 3. f(n) = n²log n log n 4. f(n) = = 5. f(n) = n n³+2 n²_n-1
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