Maclaurin’s Series Assignment Help
Urginin / Definition of Maclaurin Series
Deriving its name from Scottish mathematician named Colin Maclaurin, this series is remarked as power series which delivers approximation near the origin when applied in an arbitrary function. Precisely, its use represents equivalence to function that it is deemed to represent. Extensively studied and applied to approximate a function, it helps in gaining a closed form for the antiderivative that concerns with non-integrable function. Also, it has extensive usage in computing an uncalculatable sum wherein partial sums also leads the users to polynomial approximations for a given function.
This series is studied closely by students to expand series of a stated function and finds a special case in the Taylor series in which the functions gets expanded around zero, instead of a given value i.e. x=a. this series works with an underlying assumption that f(x) is represented as power series for x=a and features some of the determinable derivatives in all orders. If the you are stuck on completing your homework assignment of Maclurin Series, then BookMyEssay is here to provide you affordable Maclaurin’s Series assignment help.
Core Features Exhibited by Maclaurin Series
In a Maclaurin Series, every term is presented in a non-negative integer hooding the power k of a given variable precisely x, with a relatable coefficient 
. Further, in this series, a polynomial gets represented as polynomial itself. The series also supports a case arises wherein Taylor series is taken at point 0. In such a case, the formula in the series stands:
Understanding the Maclaurin Series for Function f(x) = ex?
The above listed formula is used in the similar form in the Taylor series. It helps in identifying the derivatives that relates to original function. Also, these are further used in related series as and when the need arises. Students who get assignments on this important mathematical equation has to understand the core difference that in this series, the user has to strictly take the calculation from point 0.
This is one of the most crucial sub topic covered in this series. This function is one of the most common topic to be studied in Maclaurin’s Series. This function is closely studied to find various derivatives. More than being intricate, this function is known for being an interesting study vertical wherein all derivatives represent themselves. When the first derivative is taken ex, the 2nd one is also ex, that is valued at the point 0. Keeping all the derivatives same, the users of this series evaluate ex at a range of x= 0 deriving the ultimate value of e0 = 1. This, therefore leads to the basic calculation wherein all derivatives stand equal to 1.
Points of Difference and Correlation Between Maclaurin’s and Taylor Series
In mathematics, a Taylor series can be shown as a function which carries infinite sum of terms that gets calculated from a functions’ values derivatives keeping them aligned at single point. In Taylor series, named after from Brook Taylor, an English mathematician, users can approximate the value of a function by taking into account finite number of terms. In this series, approximating a value has become a popular and common practice which further helps in yielding quantitative estimates for a stated error. A point wherein Taylor series gets transformed into a Maclaurin series is when Taylor series gets centred at point 0. The Taylor and Maclaurin series find extensive application in the field of mathematics as well as sciences.
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