Taylor expansion (one dimension)

Returns Taylor polynomial approximating a function fn(x)

taylor(fn, x0, ord = 1)

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.

Value

function.

Author

Søren Højsgaard, sorenh@math.aau.dk

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)