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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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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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