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Match the following functions with their asymptotic big- estimations. 2n + n! 100n² +n³ log (n!) √nlog (n + 2) 1. 0(n²) 2. Ⓒ(n³/²) 3. (n!) 4. (2¹) 5. O(n log n)

Match the following functions with their asymptotic big- estimations. 2n + n! 100n² +n³ log (n!) √nlog (n + 2) 1. 0(n²) 2. Ⓒ(n³/²) 3. (n!) 4. (2¹) 5. O(n log n)

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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### Match the following functions with their asymptotic big-\(\Theta\) estimations. 1. **Functions:** - \(2^n + n!\) - \(\sqrt{100n^2 + n^3}\) - \(\log (n!)\) - \(\sqrt{n \log (n + 2^n)}\) 2. **Asymptotic Big-\(\Theta\) Estimations:** - \(\Theta(n^2)\) - \(\Theta(n^{3/2})\) - \(\Theta(n!)\) - \(\Theta(2^n)\) - \(\Theta(n \log n)\) You need to match each function with the correct asymptotic big-\(\Theta\) estimation.
Transcribed Image Text:### Match the following functions with their asymptotic big-\(\Theta\) estimations. 1. **Functions:** - \(2^n + n!\) - \(\sqrt{100n^2 + n^3}\) - \(\log (n!)\) - \(\sqrt{n \log (n + 2^n)}\) 2. **Asymptotic Big-\(\Theta\) Estimations:** - \(\Theta(n^2)\) - \(\Theta(n^{3/2})\) - \(\Theta(n!)\) - \(\Theta(2^n)\) - \(\Theta(n \log n)\) You need to match each function with the correct asymptotic big-\(\Theta\) estimation.
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