Please help with the following in Time Complexity.
1)Show that the following order-of-magnitude results hold:
a)3n=O(n!)
b)(n3 -2n)/(n+1)=theta(n2)
c)n3 /log(n+1)=O(n3) but not O(n2)
2)What is wrong with the following argument?
x=O(n4),y=O(n2),therefore x/y=O(n2).
3)
What is wrong with the following argument?
x=theta(n4),y=theta(n2),therefore x/y=theta(n2).
4)Assume that f(n)=2n2 +n and g(n)=O(n2). What is wrong with the following argument?
f(n)=O(n2)+O(n), so that f(n)-g(n)=O(n2 )+O(n)-O(n2).
Therefore, f(n)-g(n)=O(n)