HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 458)

Infinite series

An infinite series has the form

. The infinite series typically

starts with indices n = 0 or n = 1. Each term in the series has a coefficient

h(n) that depends on the index n.

Taylor and Maclaurin’s series

A function f(x) can be expanded into an infinite series around a point x=x

using a Taylor’s series, namely,

(x) represents the n-th derivative of f(x) with respect to x, f

If the value x

is zero, the series is referred to as a Maclaurin’s series, i.e.,

Taylor polynomial and reminder

In practice, we cannot evaluate all terms in an infinite series, instead, we

approximate the series by a polynomial of order k, P

(x), and estimate the

order of a residual, R

(x), such that

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