title: Asymptotic complexity for typical expressions
body: <p>The increasing order of following functions shown in the picture below in terms of asymptotic complexity is:</p>
  
  <p>(A) f1(n); f4(n); f2(n); f3(n)</p>
  
  <p>(B) f1(n); f2(n); f3(n); f4(n);</p>
  
  <p>(C) f2(n); f1(n); f4(n); f3(n)</p>
  
  <p>(D) f1(n); f2(n); f4(n); f3(n)</p>
  
  <p><img src="https://i.stack.imgur.com/u1twp.png" alt="enter image description here"></p>
  
  <p>a)time complexity order for this easy question was given as--->(n^0.99)*(logn) &lt; n ......how? log might be a slow growing function but it still grows faster than a constant</p>
  
  <p>b)Consider function f1 suppose it is f1(n) = (n^1.0001)(logn) then what would be the answer?</p>
  
  <p>whenever there is an expression which involves multiplication between logarithimic and polynomial expression , does the logarithmic function outweigh the polynomial expression?</p>
  
  <p>c)How to check in such cases suppose </p>
  
  <p>1)(n^2)logn   vs  (n^1.5) which has higher time complexity?
  2) (n^1.5)logn vs (n^2)   which has higher time complexity?</p>