algorithm. please determine if the following statements are true or false? its already solved using limit rule. i want to know how to determine if the statements are true or false?

We can use limits for this purpose. The basic rules: lim f(2) g(x) =0, then f(x)=O(g(x)) if f(1) lim if ?-> g(1) =C, then f(x)=0(g(x)) f(2) lim if r-> g(x) = 0, then f(x)=12(g(x)) 6n3 6n? lim lim lim 1.n-> m2 =n-> n kloge=n-> klog2n=0c, therefore klogen =12(n2) in3 klogen n 5 + n+ 5logen 5logen 1 lim lim + lim 2.n-> nlog2n =n-> nlogin nlog2n=n-> logan =O(nlog2n)=0(nlog2n) n=0, therefore n + 5logen n2 lim k>0 3.n-> nk? =oo, when k2, n2=O(nk) 2n logan + n2 n2 n3 2n +logen n3 lim lim 4.n-> n2 =n->on2 n3 2n + log2n = 2(n2) lim n 2 logan + n n2 = 0 and hence =n->00