Taylor SeriesIf f(x) is a wellbehaved* function near a chosen expansion point, x_{0},
then the function can be expanded in a series called a Taylor series: The Taylor series for a function is often useful in physical situations to approximate the value of the function near the expansion point x_{0}. It may be evaluated termbyterm in terms of the derivatives of the function. It is typical for successive terms in a series approximation of a function to get smaller and smaller, and when the size of the next term appears negligible in terms of the problem being addressed, then one can judge that a sufficiently accurate approximation of the function has been achieved. It is often the case that a convenient expansion point is x_{0} = 0, and series about this special expansion point are also called Maclaurin series. There are many applications for expansions of common functions around x=0. Some examples are: The oneterm approximation for trig function series have many applications as "small angle approximations". * Wellbehaved means that both the function and its derivatives are defined and continuous in the range of the expansion around x_{0}. 
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