Algorithm Problem

[sydney25]

Could someone explain how to approach this problem?

True or false:

n^2 = O(n^3)

I have a bunch of problems like this and I'd just like to know how to get started. Thanks.

 

[Matt]

True. Draw graphs for both functions.

 

[sydney25]

Matt,

Thanks for the reply.

I was hoping there was an easier way then drawing graphs for all of my problems.

I think using the definition for the growth of functions takes care of the problem:

n^2 <= C*n^3 for all n>k
divide both sides by n^2
1 <= C*n for all n>k
C=1, k=1
TRUE

Do you agree?