**Problem : **
Define "abstract time".

Real time would be measured in some real unit, such as seconds. Abstract
time is measured in abstract units, such as the number of significant steps
performed in an execution of an algorithm, or the number of some significant
operations performed, such as comparisons, multiplications, copies, etc.

**Problem : **
Define "asymptotic analysis".

An asymptotic analysis of a function gives the limiting behavior of the
execution time of an algorithm, usually denoted in Big-O notation (we'll
cover this in the next section), as the size of the problem approaches
infinity. This is helpful in comparing the efficiency of two functions
given relatively large input sizes.

**Problem : **
What is the asymptotic bound of the function *f* (*n*) = 7*logn* + 2*n*^{2} + *nlogn*?

As

*n* approaches infinity, the only term that matters at all in this
equation is the

2*n*^{2}. Therefore, the asymptotic bound of this function
is

*n*^{2}.

**Problem : **
What is the asymptotic bound of the function *f* (*n*) = 100*n*^{5} +2000*n*^{4} + 18/*n*?

As

*n* approaches infinity, the dominant term in this equation is the

100*n*^{5}, so the asymptotic bound of this function is

*n*^{5}.

**Problem : **
What is the asymptotic bound of the function *f* (*n*) = 100/*n*^{2}**nlogn*.

*f* (*n*) = 100/*n*^{2}**nlogn* = 100*logn*/*n*
Therefore the asymptotic bound is

*logn*/*n*.