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Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 3n 92: n! 93 n² + n 94 n³ 95 log² n 96 log n² 97: log(n!) 98 2n+1 99 911 √n 916 n 912 log log n 917 2n 913 (n+1)! 918 nlogn ln ln n 914 Vlog n 919 5n² 910 10000 915 log √n 920 n/logn log2 n; In n = loge n; log² n = (log n)2; n! is the factorial of n, i.e., n! = 1 x 2 x. xn. Note: logn= Finally, please rank all the functions by order of growth. Present your answer in the form of: - 13m +6

Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 3n 92: n! 93 n² + n 94 n³ 95 log² n 96 log n² 97: log(n!) 98 2n+1 99 911 √n 916 n 912 log log n 917 2n 913 (n+1)! 918 nlogn ln ln n 914 Vlog n 919 5n² 910 10000 915 log √n 920 n/logn log2 n; In n = loge n; log² n = (log n)2; n! is the factorial of n, i.e., n! = 1 x 2 x. xn. Note: logn= Finally, please rank all the functions by order of growth. Present your answer in the form of: - 13m +6

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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Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 96 log n² 97 91 32 911 √n 912 log logn 917 2n 913 (n+1)! 918 nlogn 99 ln ln n 914 √log n 919 5n²-13n+6 910: 10000 915 log √n 920 n/logn Note: log n = log2 n; ln n log2 n; ln n = loge n; log² n = (log n)²; n! is the factorial of n, i.e., n! = 1 × 2 × ... xn. 92: n! 93: n² + n 94 : n³ 95 log² n (5) 98 or log(n!) 2n+1 Finally, please rank all the functions by order of growth. Present your answer in the form of: gis ✓ Gi₁gi₂..giz ~ Gi4 gi5gi16 66 gi Where gi~ 9; means gi = O(gj). gigj means g₁ = o(g;). For simplicity, you can also use "<" and "=" to represent and ~, respectively. For example, if the functions are g₁ = n², g2 = n +1,93 = n, g4 = 2". Your answer should be: n~n+1 < n² <2n, 93 92 91 94, or n=n+1 <n² <2n 916 n or 93 92 91 94 -
Transcribed Image Text:Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 96 log n² 97 91 32 911 √n 912 log logn 917 2n 913 (n+1)! 918 nlogn 99 ln ln n 914 √log n 919 5n²-13n+6 910: 10000 915 log √n 920 n/logn Note: log n = log2 n; ln n log2 n; ln n = loge n; log² n = (log n)²; n! is the factorial of n, i.e., n! = 1 × 2 × ... xn. 92: n! 93: n² + n 94 : n³ 95 log² n (5) 98 or log(n!) 2n+1 Finally, please rank all the functions by order of growth. Present your answer in the form of: gis ✓ Gi₁gi₂..giz ~ Gi4 gi5gi16 66 gi Where gi~ 9; means gi = O(gj). gigj means g₁ = o(g;). For simplicity, you can also use "<" and "=" to represent and ~, respectively. For example, if the functions are g₁ = n², g2 = n +1,93 = n, g4 = 2". Your answer should be: n~n+1 < n² <2n, 93 92 91 94, or n=n+1 <n² <2n 916 n or 93 92 91 94 -
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