1.Prove or disprove: the all-zero function f(n) = 0 is the only function that is Θ(0). 2.Give an example of a function f(n) such that f(n) = Θ(f(n) 2 ). 3. Let k ∈ Z≥0 be any constant. Prove that n k...

1.Prove or disprove: the all-zero function f(n) = 0 is the only function that is Θ(0).

2.Give an example of a function f(n) such that f(n) = Θ(f(n) 2 ).

3. Let k ∈ Z≥0 be any constant. Prove that n k = o(n!).