Prove following asymtotic notation problems.

1. 2nlog₂n + 7n = O(nlog₂n)

2. Show/ prove that 3n^{3 = O(}n⁴⁾ for specific C and N0

3. any linear function such as an + b is in O(n²)

1. 2nlog₂n + 7n = Omega(nlog₂n)

2. Show/ prove that 3n³ + n - 3= Omega(n2⁾ for specific C and N0

3. root n = Omega(n²)

1. 2nlog₂n - 3 = theta(nlog₂n)

2. Show/ prove that n²/2 - 3n = theta(n²) for specific C and N0

3. Is it true? 3n^{3 =} theta(n⁴)

4. Is it true? 2n^{2n =} theta(2ⁿ)