Show the following Asymptotic Notations: 1. 10n-3n =0(n) 2. Is 3n (n) 2 3. lg...

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Show the following Asymptotic Notations: 1. 10n²-3n =0(n²) 2. Is 3n³ € (n¹) 2 3. lg (n²) = (lgn) ? 4. Prove 22 € (2¹) 5. Is n! € 0(n") ? 6. 1,000,000 n² € Q2 (n²) ? 7. (n-1)n/2 € 2 (nr²)? 8. n/2 Q2 (²) 2 9. Show that 3n³=O(n) for appropriate c and no Q2: Find the time complexity of the following in terms of asymptotic notations: 1. for (i=0; i<N; i++) { for (j=0; i<M; itt) { sequence of statements } 2. int i =n; while (i> 0) { } for (int j = 0; j<n; j++) cout<<"*". i=1/2: 3.For (int i-n; į> 0; i-1) { For (int j=i+1; j<n; j+= 1){ St.; Show the following Asymptotic Notations: 1. 10n²-3n =0(n²) 2. Is 3n³ € (n¹) 2 3. lg (n²) = (lgn) ? 4. Prove 22 € (2¹) 5. Is n! € 0(n") ? 6. 1,000,000 n² € Q2 (n²) ? 7. (n-1)n/2 € 2 (nr²)? 8. n/2 Q2 (²) 2 9. Show that 3n³=O(n) for appropriate c and no Q2: Find the time complexity of the following in terms of asymptotic notations: 1. for (i=0; i<N; i++) { for (j=0; i<M; itt) { sequence of statements } 2. int i =n; while (i> 0) { } for (int j = 0; j<n; j++) cout<<"*". i=1/2: 3.For (int i-n; į> 0; i-1) { For (int j=i+1; j<n; j+= 1){ St.;