Questions:

1. Prove that n log n + log n ∈ O(n²).
2. Prove using only the definition of Big-Oh (and appropriate use of "≤") that 17n² log n - 60 ∈ O(n³)
3. Prove using only the definition of Big-Oh that n²- n log n ∈ O(n²)
4. Prove that if p(n) is a polynomial of degree k, then p(n) ∈ O(n^k') for any k' ≥ k, where k and k' are positive real numbers. You can use the definition of big-Oh and any other big-Oh Rules in your proof, except the polynomail rule (which this is a version of).
   
   
   
5. Show using the Rules of Big-Oh the following claim.
   
   Claim: 9n²log n + 9n log²n ∈ O(n²log n).
   
   
6. Show using the Rules of Big-Oh, and/or using the definitions of Big-Oh and Θ, the following claim.
   
   Claim: (6n²)/log n ∈ Ω(n).
   
   
7. Show using the Rules of Big-Oh, and/or using the definitions of Big-Oh and Θ, the following claim.
   
   Claim: It is not the case that (6n²)/log n ∈ O(n).
   
   
8. Show using the Rules of Big-Oh, and/or using the definitions of Big-Oh and Θ, the following claim.
   
   Claim: 0.1 n⁴log n + 2n +1 ∈ Θ(n⁴log n).