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 |$ Θ(n) - Θ(n)$ | 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)$ .