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\text { For each pairs of functions, indicate one of the three: } f=O(g), f=\Omega(g) \text {, or } f=\Theta(g) \text {. } \text { 1. } f(n)=n^{4}, g(n)=(100 n)^{3} \text { 2. } f(n)=n^{1.01}, g(n)=n^{0.99} \cdot(\log n)^{2} \text { 3. } f(n)=4 n \cdot 2^{n}+n^{100}, g(n)=3^{n} \text { 4. } f(n)=n^{2} \cdot \log \left(n^{2}\right), g(n)=n \cdot(\log n)^{3} \text { 5. } f(n)=3^{n-1}, g(n)=3^{n} \text { 6. } f(n)=1.01^{n}, g(n)=n^{2} \text { 7. } f(n)=2^{\log \log n}, g(n)=n \text { 8. } f(n)=(\log n)^{100}, g(n)=n^{0.001} \text { 9. } f(n)=5 n+\sqrt{n}, g(n)=3 n+\log n \text { 10. } f(n)=2^{n}+\log n, g(n)=2^{n}+(\log n)^{10} \text { 11. } f(n)=\sqrt[5]{n}, g(n)=\sqrt[3]{n} \text { 12. } f(n)=n !, g(n)=3^{n} \text { 13. } f(n)=\log (15 n !), g(n)=n \log \left(n^{9}\right) \text { 14. } f(n)=\sum_{k=1}^{n} k, g(n)=\log (n !) \text { 15. } f(n)=\sum_{k=1}^{n} k^{3}, g(n)=n^{3} \cdot \log n

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