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2.2 Show that (² + 4x +17) is 0(x³)

2.2 Show that (² + 4x +17) is 0(x³)

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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How would I solve this problem? I got stuck when the x^2 and the O(x^3) are different..

### Problem 2.2 **Show that** \( (x^2 + 4x + 17) \) **is** \( O(x^3) \). #### Explanation: The problem asks you to prove that the expression \( x^2 + 4x + 17 \) is asymptotically bounded by \( x^3 \) using the Big O notation. In other words, you need to demonstrate that there exists a constant \( C > 0 \) and a value \( x_0 \) such that for all \( x \geq x_0 \), the inequality \( x^2 + 4x + 17 \leq Cx^3 \) holds true.
Transcribed Image Text:### Problem 2.2 **Show that** \( (x^2 + 4x + 17) \) **is** \( O(x^3) \). #### Explanation: The problem asks you to prove that the expression \( x^2 + 4x + 17 \) is asymptotically bounded by \( x^3 \) using the Big O notation. In other words, you need to demonstrate that there exists a constant \( C > 0 \) and a value \( x_0 \) such that for all \( x \geq x_0 \), the inequality \( x^2 + 4x + 17 \leq Cx^3 \) holds true.
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