Big O, Omega, and Theta Notation: Analyzing Expression Relationships

(a) A = n^3 - 100n, B = n^2 + 50n: A = O(B), A = Ω(B)

(b) A = log2(n^2), B = log2.7(n^4): A = O(B), A = Ω(B)

(c) A = 1010000, B = n: A = O(B), A = Ω(B)

(d) A = 2nlogn, B = n^10 + 8n^2: A = O(B), A = Ω(B)

(e) A = 2^n, B = 2^(n+logn): A = O(B), A = Ω(B)

(f) A = 3^(3n), B = 3^(2n): A = O(B), A = Ω(B)

(g) A = (√2)^logn, B = √logn: A = O(B), A = Ω(B)