Hello I've tried my best to understand big-theta and now I get the main conception of the proofs for Big-Oh and Big-Omega but i couldn't find and example that is close to my excercise, because i cant do the proof for that one:
Prove, by exhibiting witnesses, that 4n^2 + 4n = Big-Theta(2n^2 + 32n)
I know that i have to prove it for Big-Oh and Big-Omega in order to prove Big-Theta, but i have no idea how to start. I mean the equation on the right side confuses me.
By the definition of big-theta, you need to show that there exist two constants, k1 and k2, such that for all sufficiently large values of n,
k1 * |2n^2 + 32n| <= |4n^2 + 4n| <= k2 * |2n^2 + 32n|
(Since your functions are all positive for positive n, you can drop the absolute values.) Just show that each inequality can be satisfied separately and you're done.