doBy (version 4.6.22)

taylor: Taylor expansion (one dimension)

Description

Returns Taylor polynomial approximating a function fn(x)

Usage

taylor(fn, x0, ord = 1)

Value

function.

Arguments

fn

A function of one variable and that variable must be named 'x'.

x0

The point in which to to the Taylor expansion.

ord

The order of the Taylor expansion.

Author

Søren Højsgaard,

Examples

fn <- function(x) log(x)
ord <- 2
x0 <- 2

xv  <- seq(.2, 5, .1)
plot(xv, fn(xv), type="l")
lines(xv, taylor(fn, x0=x0, ord=ord)(xv), lty=2)
abline(v=x0)

fn <- function(x)sin(x)
ord <- 4
x0 <- 0
xv <- seq(-2*pi, 2*pi, 0.1)
plot(xv, fn(xv), type="l")
lines(xv, taylor(fn, x0=x0, ord=ord)(xv), lty=2)
abline(v=x0)