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Asymptotic Analysis Problems Conventions: lgn=log2nlnn=logcnlogn=log10nlogcn=(logn)clglgn=lg(lgn) Using the asymptotic definitions or the limit theorem, prove (or disprove) the following statements. 1. 32nO(n) 2. lnn(n) 3. lgn(lnn)

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Asymptotic Analysis Problems Conventions: lgn=log2nlnn=logcnlogn=log10nlogcn=(logn)clglgn=lg(lgn) Using the asymptotic definitions or the limit theorem, prove (or disprove) the following statements. 1. 32nO(n) 2. lnn(n) 3. lgn(lnn) 4. logcn(lnn),c>1 5. n2O(2n) 6. n3(n2) 7. 4lgn(n) 8. ln2nO(n) 9. ln2nO(n) 10. lncnO(nk),ck>0 11. In lnnO(lnn) 12. 2n(2n+1)

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