Lab 05 - Asymptotic notations

1.1 If $ f \in O(n \sqrt n)$ and $ g \in Θ(n)$ then $ f \over g$ in ?

1.2 If $ f \in Θ(n)$ and $ g \in O(\sqrt n)$ then $ f \over g$ in ?

1.3 $ $ in ?

2.1 Prove that if lim $ g(n) \over f(n)$ = 0 implies that g(n) in o(f(n)), for n reaching infinity. Hint: use the “epsilon” or “Cauchy” limit definition for sequences.

2.2 Prove that f(n) in Ω(log(n)) and g(n) in O(n) implies f(n) in Ω(log(g(n))).

2.3 Prove that f(n) $ \in$ Ω(g(n)) and g(n) $ \in$ $ O(n ^ 2)$ , then $ g(n) \over f(n)$ [\in] O(n).