Taylor Expansion  
If a function has continuous derivatives up to (n+1)^{th} order, then this function can be expanded in the following fashion:
where , called the remainder after n+1 terms, is given by: When this expansion converges over a certain range of , that is, , then the expansion is called the Taylor Series of expanded about . If the series is called the MacLaurin Series:

Some Useful Taylor Series  
