There is a hint for each questions What are the big-O notations for the following functions? Show your proofs.(B4) n³ log(3n) + 2nª + 3n² + 127(B5) V2n + 30 log(4n)² + 27n – 3(B6) (n + 1)! + 2"(B7) Vn2 + 3n log²(2n) + 4n7 B4. n³ log(3n) + 2nª + 3n² + 127What will be the leading term? What is of higher order n³log(3n) or 2n*? Orequivalently, log(3n) vs n. Recall the long-term log property in Lecture 03.Hint: Big-O (n*)2n* < 2 x n*n³ log(3n) < 1 x n* (when n 2 ?)3n? < 3 × n* (when n2?)127 < 127 × n* (when n >?)B5. V2n + 30 log(4n) + 27n – 3 = v2 x n7 + 30 log(4n) + 27n – 3Hints: Big-0 (n)B6. Hint: Big-O((n + 1)!)2B7. Vn? + 3n log²(2n) + 4n7 = n3 + 3n log²(2n) + 4n7Hint: Big-0 (n log²(2n))

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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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What are the big-O notations for the following functions? Show your proofs. (B4) n³ log(3n)+ 2nª + 3n² + 127 (B5) V2n + 30log(4n)² + 27n – 3 (В6) (п + 1)! + 27 (B7) Vn2 + 3n log²(2n) + 4n7