title: Big Oh Notation and Big Theta Notation Simplifying
body: <p>I have a homework question that asked us to show that 2n+5 is O(n²).</p>
  
  <p>This is what I did to try and solve it:</p>
  
  <p>I chose that k = 1 and assumed that n > 1 so then
  f(n)/g(n) = (2n+5)/n² &lt; (2n+5n)/n² = 7n/n² = 7/n</p>
  
  <p>So, therefore C is equal to 7/n
  Therefore, 2n+5 &lt;= (7/n)(n²) so 2n+5 &lt;= 7n which is true for all n > 1. 
  That is why 2n+5 is O(n²). </p>
  
  <p>I just wasn't sure if that was correct or not. I'm not 100% sure, but if anyone could confirm that would be great.</p>
  
  <p>Also, I got confused on another problem that asked to simplify to theta notation: </p>
  
  <p>(x<sup>4.2</sup>)/(1+x²). Is that just Θ(x<sup>2.2</sup>) since I just evaluated it to infinity?</p>
  
  <p>Also, x³⋅lg(x) I have no clue where to start for that.</p>
  
  <p>Thanks in advance!</p>