algorithmbig-onotationasymptotic-complexitylittle-o

Trouble understanding little-o notation example

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?

Solution

  • definition of little o is

    enter image description here 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.