Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Big-O Notation Let fand g be functions from the set of integers or the set of real numbers to the set of real numbe We say that f ( x ) is 0 (g (x)), read as "f ( x ) is big-oh of g (x )", if there are constants Cand k such that | f(x) |s C|g(x) | whenever x > k. (a) Show that f(x) = x2 + 2x + 1 is 0(x2) Solution:

1. Big-O Notation Let fand g be functions from the set of integers or the set of real numbers to the set of real numbe We say that f ( x ) is 0 (g (x)), read as "f ( x ) is big-oh of g (x )", if there are constants Cand k such that | f(x) |s C|g(x) | whenever x > k. (a) Show that f(x) = x2 + 2x + 1 is 0(x2) Solution:

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
See similar textbooks
icon
Related questions
Question

Given the explanation below please answer the number 2
Thank you!
Subject: Discrete Mathematics
Lesson: Big-O Notation

 

1. Big-O 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 )|sClg(x)|whenever x > k. (a) Show that f(x) = x2 + 2x + 1 is 0(x2) Solution: When x>1; * (1) * (1+) - x2 x2 = 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)=x? 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 0(x*).
Transcribed Image Text:1. Big-O 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 )|sClg(x)|whenever x > k. (a) Show that f(x) = x2 + 2x + 1 is 0(x2) Solution: When x>1; * (1) * (1+) - x2 x2 = 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)=x? 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 0(x*).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS