PROBLEM 1 1. $f(n)=}, g(n)=lg(7^{2n})$ f(n)=27n/2, g(n)=2nlg(7) f(n)=lg(27n/2),g(n)=lg(2nlg(7)) f(n)=lg(27n/2),g(n)=lg(2nlg(7)) f(n)=7n/2, g(n)=lg(2n)+lg(lg(7)) f(n)=7n/2, g(n)=lg(2n) f = Ω(g) 2. f(n)=2nln(n), g(n)=n! f(n)=ln(2nln(n)),g(n)=ln(n!) f(n)=nln(n),g(n)=nlg(n) (via previously proved identity) f = θ(g) 3. f(n)=lg(lg*n),g(n)=lg*(lgn) f = O(g) 4. $f(n)={n},g(n)=lg^*n$ f = O(g) via limits. f approaches 0. 5. f(n)=2n, g(n)=nlgn f(n)=n, g(n)=(lgn)² f = Ω(g) 6. $f(n)=2^{}, g(n)=n(lgn)^3$ f(n)=(lgn)1/2, g(n)=lg(n)+lg((lg(n))³) f = O(g) 7. f(n)=ecos(n), g(n)=lgn f(n)=cos(n),g(n)=ln(lg(n)) f = O(g) 8. f(n)=lgn², g(n)=(lgn)² f(n)=2lg(n),g(n)=(lgn)² f = O(g) 9. $f(n)=, g(n)=n^({2})$ $f(n)=2n, g(n)=n^({2})$ f(n)=O(g) 10. $f(n)=^{n} k, g(n)=(n+2)^2$ $f(n) = {2}$ via summation formula g(n)=(n + 2)² f = θ(g)