A function f(x) is (g(x)) if and only if there are positive constants k, C₁, and C₂ such that C₁lg(x) ≤ f(x)| ≤ C₂lg(x) whene x> K. Click and drag the steps in the correct order to show that 3x² + x + 1 is ©(x²). (You must provide an answer before moving to the next part.) 3x² + x + 1 is 0(3x²) since 3x² is O(3x² + x + 1) since Thus, 3x² + x + 1 is (3x²). 3x² 3x² + x + 1 for x > 0. Take k = 1, C, = 1, and C₂ = 2. Then, 1 3x² ≤ 3x² + x + 1 ≤ 2 3x² for all x > 0. Then, 1 3x² ≤ 3x² + x + 1 ≤2 3x² for all x> 1. 3x² + x + 1 ≤ 3x² + 3x²= 2 3x² for all x>1. Take k = 0, C₁ = 1, and C₂ = 0.
A function f(x) is (g(x)) if and only if there are positive constants k, C₁, and C₂ such that C₁lg(x) ≤ f(x)| ≤ C₂lg(x) whene x> K. Click and drag the steps in the correct order to show that 3x² + x + 1 is ©(x²). (You must provide an answer before moving to the next part.) 3x² + x + 1 is 0(3x²) since 3x² is O(3x² + x + 1) since Thus, 3x² + x + 1 is (3x²). 3x² 3x² + x + 1 for x > 0. Take k = 1, C, = 1, and C₂ = 2. Then, 1 3x² ≤ 3x² + x + 1 ≤ 2 3x² for all x > 0. Then, 1 3x² ≤ 3x² + x + 1 ≤2 3x² for all x> 1. 3x² + x + 1 ≤ 3x² + 3x²= 2 3x² for all x>1. Take k = 0, C₁ = 1, and C₂ = 0.
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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Transcribed Image Text:A function f(x) is (g(x)) if and only if there are positive constants k, C₁, and C₂ such that C₁lg(x)| ≤ f(x)| ≤ C₂lg(x) whenever
S
x> K.
Click and drag the steps in the correct order to show that 3x² + x + 1 is ©(x²).
(You must provide an answer before moving to the next part.)
3x² + x + 1 is 0(3x²) since
3x² is O(3x² + x + 1) since
Thus, 3x² + x + 1 is (3x²).
3x² ≤ 3x² + x + 1 for x > 0.
Take k = 1, C₁ = 1, and C₂ = 2.
Then, 1.3x² ≤ 3x² + x + 1 ≤ 2 3x² for all x > 0.
Then, 1.3x² ≤ 3x² + x + 1 ≤2· 3x² for all x> 1.
3x² + x + 1 ≤ 3x² + 3x²= 2 3x² for all x>1.
Take k = 0, C₁ = 1, and C₂ = 0.
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