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\title{Class work: Asymptotic notation}

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\item  (R-1.2) Algorithm A uses $10 n \lg n$ operations, while algorithm B
  uses $n^2$ operations. Determine the value $n_0$ such that A is
  better than B  for $n \ge n_0$. 

\item (R-1.7) Let $f(n) = \lg n$  and assume that we have an
  algorithm whose running time is $f(n)$ microseconds.  Determine the largest size of a problem
  that can be solved by the algorithm in: (a) 1 second; (b) 1 hour;
  (c) 1 month; (d) 1 century. 


  Same problem for $f(n) = \sqrt n$ and $f(n) = n$. 

\item (R-1.6) Order the following expressions from fastest to slowest: 
  
$$ \sqrt 2 ^ {\lg n}, n^2, {(\frac{3}{2})}^n, n^3, \lg n ^2,  \lg^2 n,  2^n, \lg \lg n, n \lg n$$



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