taylor function

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.

Returns

function.

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)

Author(s)

Søren Højsgaard, sorenh@math.aau.dk