Can you solve this discrite math and computer science questions? with solutions and explainitions .

Select the best "big Oh" notation for each expression. Justify by showing the constants c and n_0- Note that f(n) = O(g(n)) if there are constants c > 0 and n_0 > 0 so that for all n greaterthanorequalto n_0 we have |f(n)| lessthanorequalto c middot g(n). 1. 100 n^2 + n. 2. (15n + log n)^3. 3. 3n^5 - 5n^2 - 100. n^2 log n + n+ squareroot n + log n. Show the following: 5n^2 - n log n = theta (n^2) n^2 log^3 n + 1 = O(n^3) Justify that n log n log n + squareroot n is not O (n). We say that f(n) precedes g(n) if g (n) grows faster than f(n) (e.g., log n precedes n). Order the following functions by by precedes from the lowest to the highest: (3/2)^n, 100, n^2 log n, 2^log_2 n, log^2 n, 2^2 log_2 n, 2^n. Justify your