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What will happen to the term 2x + 5 of the original function x² + 2x + 5 when compared to the dominant term which is x². Show a simple analysis for this function.

What will happen to the term 2x + 5 of the original function x² + 2x + 5 when compared to the dominant term which is x². Show a simple analysis for this function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given the explanation below please answer the number 6
Thank you!
Subject: Discrete Mathematics
Lesson: Big-O Notation

6. What will happen to the term 2x + 5 of the original function x2 + 2x + 5 when compared to the dominant term which is x2. Show a simple analysis for this function.
Transcribed Image Text:6. What will happen to the term 2x + 5 of the original function x2 + 2x + 5 when compared to the dominant term which is x2. Show a simple analysis for this function.
1. Big-0 Notation Let fand g be functions from the set of integers or the set of real numbers to the set of real 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 )|s Clg (x)| whenever x > k. (a) Show that f(x) = x² + 2x + 1 is 0(x?) Solution: When x>1; 1 +-+ < x2 1 + + = 4x2 So, for x > 1, x? + 2x +1< 4x? From the definition 0 s f(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? 3D Therefore, x? + 2x +1 = 0(x?) O(g(x)) = (f(x)|there exist positive constant c and No such that 0s f(x) s cg(x) for all x2No} 2. Show that 7x2 is 0(x*). 3. Suppose there are x number of boxes to be delivered to x number of household that is 2km apart, what is the distance travelled by the transport delivery service? 4. In number 3, suppose that each boxes must be coming from the Warehouse and the transport delivery service must need to back-and-port to pick-up each box. What is the distance travelled by the transport delivery service? 5. Evaluate the methods used in number 3 and number 4 method of delivery. If the function x² is considered as the dominant term for each method used.
Transcribed Image Text:1. Big-0 Notation Let fand g be functions from the set of integers or the set of real numbers to the set of real 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 )|s Clg (x)| whenever x > k. (a) Show that f(x) = x² + 2x + 1 is 0(x?) Solution: When x>1; 1 +-+ < x2 1 + + = 4x2 So, for x > 1, x? + 2x +1< 4x? From the definition 0 s f(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? 3D Therefore, x? + 2x +1 = 0(x?) O(g(x)) = (f(x)|there exist positive constant c and No such that 0s f(x) s cg(x) for all x2No} 2. Show that 7x2 is 0(x*). 3. Suppose there are x number of boxes to be delivered to x number of household that is 2km apart, what is the distance travelled by the transport delivery service? 4. In number 3, suppose that each boxes must be coming from the Warehouse and the transport delivery service must need to back-and-port to pick-up each box. What is the distance travelled by the transport delivery service? 5. Evaluate the methods used in number 3 and number 4 method of delivery. If the function x² is considered as the dominant term for each method used.
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