Edit this page Backlinks This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Lab 05 - Asymptotic notations ====== ==== 1. Asymptotic notations ==== **1.1** If $math[f \in O(n \sqrt n)] and $math[g \in Θ(n)] then $math[f \over g] in ? **1.2** If $math[f \in Θ(n)] and $math[g \in O(\sqrt n)] then $math[f \over g] in ? **1.3** |$math[Θ(n) - Θ(n)]| in ? ==== 2. Properties of asymptotic notations ==== **2.1** Prove that if $math[lim] $math[g(n) \over f(n) = 0] implies that $math[g(n) \in o(f(n))], for n reaching infinity. Hint: use the "epsilon" or "Cauchy" limit definition for sequences. **2.2** Prove that $math[f(n) \in Ω(log(n))] and $math[g(n) \in O(n)] implies $math[f(n) \in Ω(log(g(n)))]. **2.3** Prove that $math[f(n) \in Ω(g(n))] and $math[g(n) \in O(n ^ 2)], then $math[g(n) \over f(n)] $math[\in O(n)]. **2.4** $math[O(n) \cap Ω(n) = Θ(n)] ?