REMAINDER TERM Meaning and
Definition
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The term "remainder term" refers to a concept within mathematical and statistical calculations, particularly in the field of calculus. It represents the discrepancy or error between an exact value and an approximation. More specifically, it is the residual amount which remains after subtracting an approximated value from the actual value.
In calculus, the remainder term is often utilized in Taylor series expansions. This series represents a polynomial approximation of a function around a given point. The remainder term calculates the difference between the actual value of the function and the value predicted by the Taylor series at a particular point. It is crucial because it provides an estimation of the error introduced by truncating the series to a finite number of terms.
The remainder term is commonly expressed as a function of the degree of approximation or as an inequality that bounds the error. These forms enable mathematicians and statisticians to determine the accuracy of their approximations. By analyzing the properties of the remainder term, such as its convergence or divergence, they can assess the reliability of their calculations.
Understanding the remainder term is vital in calculus and other mathematical disciplines as it allows for more precise and reliable estimations. By accounting for the discrepancy between approximation and actual values, mathematicians can improve the accuracy of their computations and minimize errors in their results.
Etymology of REMAINDER TERM
The word "remainder" originated from the Middle English word "remaundre", which was derived from the Old French word "remaindre", meaning "to remain" or "to stay behind". Its Latin root is "remanere", where "re-" indicates "again" or "back" and "manere" means "to stay" or "to remain".
The term "remainder term" likely emerged in the context of mathematics or algebra. In mathematics, the remainder term refers to the error or difference between the original function and its approximation when using a finite number of terms in a series or expansion. The term "remainder" is used to signify what remains or is left after taking into account the existing terms or approximation.
