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 lim $math[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) $math[\in] Ω(g(n)) and g(n) $math[\in] $math[O(n ^ 2)], then $math[g(n) \over f(n)] [\in] O(n).