Taylor Series Approximations

Load Package

library(pracma)

## Warning: package 'pracma' was built under R version 4.2.2

f(x) = 1/(1-x)

f1 <- function(x) { 1 / (1 - x) }
a1 <- 0
n1 <- 5
taylor(f1,a1,n1)

## [1] 1.000293 1.000029 1.000003 1.000000 1.000000 1.000000

f(x) = e^x

f1 <- function(x) { exp(x) }
a1 <- 0
n1 <- 5
taylor(f1,a1,n1)

## [1] 0.008334245 0.041666573 0.166666726 0.499999996 1.000000000 1.000000000

f(x) = ln(1 + x)

f1 <- function(x) { log(1 + x) }
a1 <- 0
n1 <- 5
taylor(f1,a1,n1)

## [1]  0.2000413 -0.2500044  0.3333339 -0.5000000  1.0000000  0.0000000

f(x) = x^(1/2)

f1<- function(x) { x^1/2 }
a1 <- 0
n1 <- 4
taylor(f1,a1,n1)

## [1] 0.5 0.0