Master Theorem: Why is T(n)=16T(n/4)+n! considered Θ(n!)

I am having some problem trying to understand why T(n)=16T(n/4)+n! is consideredΘ(n!) I am using the following master theorem below from here:https://www.geeksforgeeks.org/advanced-master-theorem-for-divide-and-conquer-recurrences/The confusing part here is that my friend says that the answer is actually O(n!) and not Θ(n!)... So I am really confused....Read more

Master theorem with logn

Here's a problem.I am really confused about the c being equal to 0.5 part. Actually overall I am confused how the logn can become n^(0.5). Couldn't I just let c be equal to 100 which would mean 100 < d which results in a different case being used? What am I missing here?...Read more

master theorem - Difficulty figuring out the time complexity of this recursive function

I think it's interesting but I'm not sure about my solution. This algorithm calculates xnIf I use the master theorem my reasoning goes like thisT(n) = 2 T(n/2) + f(n)But f(n) in this case is 1? Because n <= 4 is constant. Gives me:T(n) = Θ(n)If I use substitution I get this answerT(n) = Θ(n + log(n))I think I'm doing lots of things wrong. Can someone point me in the right direction?...Read more