In: Computer Science
Determine if the following statements are true or false.
In either case, provide a formal proof using the definitions of the big-O, big-Omega, and big-Theta notations. For instance, to formally prove that f (n) ∈ O(g(n)) or f (n) ∉ O(g(n)), we need to demonstrate the existence of a constant c and a sufficient large n0 such that f (n) ≤ c g(n) for all n ≥ n0, or showing that there are no such values.
a) 10000n2 ∈ O(n4). (Big O)
b) 2nn2 ∈ Ω(3n). (Big
Omega)
c) sqroot(3n2 + 4n) ∈ Θ(n). (Big Theta)
Could i please ask to see hand written working if possible?? Helps me understands better ! Thanks