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Question: 1 2 3 4 by definition of big 0 tn...

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1) 2) 3) 4) By definition of Big 0, T(N) EO(g(N)), show that 100*N+5 E0(N2) By definition of Big S2, T(N) E Ω (g(N)) , show that NE Ω (N*) By definition of Big Θ, T(N) E Θ (g(N)), show tha1% *N *(N-1) E Θ (N2) Using Limits for order of growth (LΉ0pitals Rule), show N *N-1) E Θ (N*), explain why 5) Using Limits for order of growth (LHopitals Rule), show log2 NE o (VN) (little-oh notation), explain why 6) Using Limits for order of growth (LHopitals Rule), show N! E 2 (2N), explain why V(2*π * N) * (N/e) Stirlings formula states N! 7) Order the following functions according to heir order of growth (from the lowest to highest): (n-2)!, 5log(n+100)10, 2(2-N), 0.001*N4 +3n3+1, VN, 3N

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