**<< Previous page TOC INDEX Next page >>**

Formal Statement of Taylor’s TheoremLet be continuous on a real interval containing (and ), and let exist at and be continuous for all . Then we have the following Taylor series expansion:

where is called the remainder term. There exists between and such that

In particular, if in , then

which is normally small when is close to .When , the Taylor series reduces to what is called a Maclaurin series.