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Consider the function f(x) = 24x³ + 3x² + 8x + 12. Show that f(x) is 0(x²) by determining a pair of witnesses that proves the big-O relation. (Hint: When x > 1, note that x> log₂ x.)

Consider the function f(x) = 24x³ + 3x² + 8x + 12. Show that f(x) is 0(x²) by determining a pair of witnesses that proves the big-O relation. (Hint: When x > 1, note that x> log₂ x.)

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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### Big-O Notation: Example and Witness Pair Determination Consider the function \( f(x) = 24x^3 + 3x^2 + 8x + 12 \). Show that \( f(x) \) is \( O(x^2) \) by determining a pair of witnesses that proves the big-O relation. *Hint: When \( x > 1 \), note that \( x > \log_2 x \).*
Transcribed Image Text:### Big-O Notation: Example and Witness Pair Determination Consider the function \( f(x) = 24x^3 + 3x^2 + 8x + 12 \). Show that \( f(x) \) is \( O(x^2) \) by determining a pair of witnesses that proves the big-O relation. *Hint: When \( x > 1 \), note that \( x > \log_2 x \).*
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