Difference between Taylor and MacLaurin Series-Usage

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SUMMARY

The discussion clarifies that the Maclaurin series is a specific case of the Taylor series, centered at x=0. While both series can be used for approximating functions, the Taylor series is often more effective for values closer to its center, such as using the Taylor series centered at x=2 to approximate f(2.1). The participants emphasize that the terms "Taylor and Maclaurin series" refer to their respective polynomials when truncated, and there is no inherent accuracy difference between the two series themselves.

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Hi all,

I understand the numerical difference between a Taylor and Maclaurin Series; Maclaurin series is just Taylor Series about x=0. However, is there any difference between their usage?

I'm guessing Taylor series may be more accurate with less terms for approximating something close to its center; ex. finding f(2.1) for Taylor series about x=2 rather than using Maclaurin series. Am I correct in this assumption? What makes using one better than using the other?

Thanks.
 
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Yes it may be better to use the series about 2 to find f(2.1) than the series about 0. We can do this with the Maclaurin Series though just find the series about 0 of f(x+2)

Since the Taylor series about a of f(x) is the same as the Maclaurin series of f(x+a) the two can be considered the same.
 
A word about terminology: you are really talking about Taylor and MacLaurin polynomials (truncated series) not the series themselves. There is no question of "accuracy" with Taylor and MacLaurin series.
 

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