函数增长率
[英]Growth rate of the functions
问题描述
I am trying to order functions according to their growth rate but I am stuck here.
我正在尝试根据其增长率订购功能，但我被困在这里。 y=5^{n}, y=(n,)^{n} , y=(n^{2})! y=5^{n}, y=(n,)^{n} , y=(n^{2})！
5^{n} is exponential I am assume this is bigger but I cannot proof that. 5^{n} 是指数的，我认为这更大，但我无法证明这一点。 When looking at their graphs it seems like (n^{2}).当查看他们的图表时，它看起来像 (n^{2})。 is bigger I cannot understand.更大我无法理解。 Help pls.请帮忙。
1 个解决方案
解决方案1
1 2020-11-28 21:24:35
Take the logarithms.取对数。 This will tel you work with the much more manageable functions (keep in mind the Stirling approximation log(n!) ~= n * log(n) ):这将告诉您使用更易于管理的功能（请记住斯特林近似log(n!) ~= n * log(n) ）：
n * log(5)
n * log(n!) ~= n^2 * log(n)
n^2 * log(n^2) = 2 n^2 * log(n)
Can you continue?你能继续吗？
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