Trouble understanding little-o notation example

Question

I'm having trouble with this one problem

9n <= cn^3

basically I can get down to

9/c <= n^2

But how do I solve the rest?

Answer 1

definition of little o is

we say f(x)=o(g(x)).

let f(x)=9*x and g(x)=c*x^3 where c is a positive constant. when x tends to infinity, f(x)/g(x) tends to 0.so we can say f(x)=o(g(x)).

asyptotic notations are applicable for sufficiently large value of n.so for large value of n

9n << cn^3

for all c>0.

Answer 2

Read this link to undersatnd big-O and little-O link

see in case of your equation, when n=3 it becomes 9*3=23=3^3 so for n<3 9n > n^3. so if you choose c as any number to make 9n<=n^3 for n<3 then it can be in O(n).