title: Can't calculate growth rate of function
body: <p><a href="https://i.stack.imgur.com/O9aIs.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/O9aIs.png" alt="enter image description here"></a></p>
  
  <p>Hello, I am trying to solve a question in above image, but I can't.</p>
  
  <p>Specially, my question is about C(n) in the image, I got "7logn + n^(1/3)" at the end. </p>
  
  <p>we know that left side of + sign, "7logn&lt;=n for all n>7 (witness c=1, k=7)", and right side of + sign, "n^(1/3)&lt;=n". </p>
  
  <p>Both sides between + sign from my perspective is O(n) and thus whole C(n) is O(n). </p>
  
  <p>But why the answer is Big-theta(n^1/3)?</p>