Analysis
In this section, we recap the notation that is used in analyzing and describing the behavior of functions. This includes notation for describing limits, notation for describing the relative ordering of functions, and notation for describing standard approximations of functions.
Limits
When we are talking about limits, we are talking about the mathematical behavior of some quantity, often a function, as some other quantity approaches a particular value, often infinity. Let’s make that more concrete. Consider the function 
. As 
gets bigger and bigger, then clearly, the value of 
gets smaller and smaller, until eventually, as becomes infinitely large, becomes zero. We say that 
approaches its limit of 0 as approaches 
. Mathematically, we write this as follows:
Eq. 46
The word lim denotes the fact that we are talking about a limit, while the symbols 
describe what limit we are talking about. The RHS of Eq. 46 gives the actual limiting value.
Sometimes...
