Big Theta

Unfortunately, I have not had a chance to solve a proof involving Big Theta, it's that time of the year where I'm nocturnal, and making an 11am class seems impossible (unfortuantely).

Of course, Danny Heap was a great professor, so I always made an effort to go, In fact, I may have broken a personal record in how many lectures attended for a course.

Anyway.

I will attempt to solve a Big Theta proof in the following post.

Prove that 5n^3 - 3n^2 + 2n + 3 in in Big Theta(2n^3 - n^2 + n + 1)

Case 1:

Case 2:

Then 5n^3 - 3n^2 + 2n + 3 in Big O(2n^3 - n^2 + n + 1)  AND 5n^3 - 3n^2 + 2n + 3 in Big Omega (2n^3 - n^2 + n + 1) 

Hence 5n^3 - 3n^2 + 2n + 3 in Big Theta(2n^3 - n^2 + n + 1)