在FRAXIS提供的文件中
https://goo.gl/t5ZSz6
p.1
Exercise 1 (YZU CSIE 90)
1. Prove or disprove
n^[2 + sin(n)/lg n] = O(n^2)
我算出的結果與文件中相反，請問我哪裡錯了?
consider n>1
sin(n)/lg n <= 1/lg n
n^[sin(n)/lg n]
<= n^[1/lg n]
= [2^(lg n)]^[1/lg n]
= 2^[(lg n)*(1/lg n)]
= 2
n^[2 + sin(n)/lg n]
= n^2 * n^[sin(n)/lg n]
<= n^2 * 2
所以 n^[2 + sin(n)/lg n] = O(n^2)