Untitled

library(calculus)

## Warning: package 'calculus' was built under R version 4.3.3

f(x) = 1 - x

taylor_f1 <- taylor(f = expression(1 - x), var = "x", order = 5)
print(taylor_f1)

## $f
## [1] "(1) * 1 + (-1) * x^1"
## 
## $order
## [1] 5
## 
## $terms
##   var coef degree
## 0   1    1      0
## 1 x^1   -1      1
## 2 x^2    0      2
## 3 x^3    0      3
## 4 x^4    0      4
## 5 x^5    0      5

f(x) = exp(x)

taylor_f2 <- taylor(f = expression(exp(x)), var = "x", order = 5)
print(taylor_f2)

## $f
## [1] "(1) * 1 + (1) * x^1 + (0.5) * x^2 + (0.166666666666667) * x^3 + (0.0416666666666667) * x^4 + (0.00833333333333333) * x^5"
## 
## $order
## [1] 5
## 
## $terms
##   var        coef degree
## 0   1 1.000000000      0
## 1 x^1 1.000000000      1
## 2 x^2 0.500000000      2
## 3 x^3 0.166666667      3
## 4 x^4 0.041666667      4
## 5 x^5 0.008333333      5

#f(x) = ln(1 + x)

taylor_f3 <- taylor(f = expression(log(1 + x)), var = "x", order = 5)
print(taylor_f3)

## $f
## [1] "(1) * x^1 + (-0.5) * x^2 + (0.333333333333333) * x^3 + (-0.25) * x^4 + (0.2) * x^5"
## 
## $order
## [1] 5
## 
## $terms
##   var       coef degree
## 0   1  0.0000000      0
## 1 x^1  1.0000000      1
## 2 x^2 -0.5000000      2
## 3 x^3  0.3333333      3
## 4 x^4 -0.2500000      4
## 5 x^5  0.2000000      5

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

taylor_f4 <- taylor(f = expression(x^(1/2)), var = "x", order = 5)
print(taylor_f4)

## $f
## [1] "(Inf) * x^1 + (-Inf) * x^2 + (Inf) * x^3 + (-Inf) * x^4 + (Inf) * x^5"
## 
## $order
## [1] 5
## 
## $terms
##   var coef degree
## 0   1    0      0
## 1 x^1  Inf      1
## 2 x^2 -Inf      2
## 3 x^3  Inf      3
## 4 x^4 -Inf      4
## 5 x^5  Inf      5