Let fand g be functions from the set of integers or the set of real numbers to the set ofreal numbers. We say that f (x ) is 0 (g (x)), read as "f(x) is big-oh of g ( x)", if there are constants C and k such that | f (x)|SCI8(x)|whenever x>k. (a) Show that f(x) =x? + 2x + 1 is O(x*) Solution: When x>1: So, for x > 1,x² + 2x +1< 4x² From the definition 0 s ({x) s cg(x) for x21 Hence, for No = 1; c=4; and g(x)=x2 for No = 2: c=3: and g(x)=x for No = 3; c=2; and g(x)=x? Therefore, x? + 2x +1=0(x²) O(g(x)) = {f(x)]there exist positive constant c and No such that 0 s f(x) S cg(x) for all x2No} 2. Show that 7x2 is O(x³). 3. Suppose there are x number of boxes to be delivered tox number of household that is 2km apart, what is the distance travelled by the transport delivery service?

Let fand g be functions from the set of integers or the set of real numbers to the set ofreal numbers. We say that f (x ) is 0 (g (x)), read as "f(x) is big-oh of g ( x)", if there are constants C and k such that | f (x)|SCI8(x)|whenever x>k. (a) Show that f(x) =x? + 2x + 1 is O(x*) Solution: When x>1: So, for x > 1,x² + 2x +1< 4x² From the definition 0 s ({x) s cg(x) for x21 Hence, for No = 1; c=4; and g(x)=x2 for No = 2: c=3: and g(x)=x for No = 3; c=2; and g(x)=x? Therefore, x? + 2x +1=0(x²) O(g(x)) = {f(x)]there exist positive constant c and No such that 0 s f(x) S cg(x) for all x2No} 2. Show that 7x2 is O(x³). 3. Suppose there are x number of boxes to be delivered tox number of household that is 2km apart, what is the distance travelled by the transport delivery service?

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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