7. Let f(n)> g(n) denote that the first derivative of f(n) is larger than that of g(n). (25) Let f(n)> g(n) denote that f(n) is asymptotically larger than g(n). Let f(n)> g(n) denote that f(n) is polynomially larger than g(n). Note that exponentially greater also qualifies as polynomially greater. Similarly, << < are defined. Fill in the blanks with one or more of (>, >a, >, <, <, p<, 8) and briefly justify. (1) n log n (ii) n log n (iii) 2n (iv) 2n (v) n³ + 3n²+1000. D n¹.1 n²0 n! n logn + n³/6

7. Let f(n)> g(n) denote that the first derivative of f(n) is larger than that of g(n). (25) Let f(n)> g(n) denote that f(n) is asymptotically larger than g(n). Let f(n)> g(n) denote that f(n) is polynomially larger than g(n). Note that exponentially greater also qualifies as polynomially greater. Similarly, << < are defined. Fill in the blanks with one or more of (>, >a, >, <, <, p<, 8) and briefly justify. (1) n log n (ii) n log n (iii) 2n (iv) 2n (v) n³ + 3n²+1000. D n¹.1 n²0 n! n logn + n³/6

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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6. Suppose functions f(n) > 0 and g(n) > 0 satisfy f(n) = 0(9(n)). Prove or give a counterexample to each of the following. (a) log, f(n) = O(log, 9(n)). To avoid an obscure special case, assume that g(n) > 2 for all n. (b) 2/(n) = 0(29(n)) %3D %3D (c) (f(n))² = 0(g(n))")