Pick any exercise in 8.8 of the calculus textbook. Solve and post your solution. If you have issues doing so, discuss them.
library(calculus)
taylor("atan(x/2)", 0, var = "x", order = 9)
## $f
## [1] "(0.5) * x^1 + (-0.0416666666666667) * x^3 + (0.00625) * x^5 + (-0.00111607142857143) * x^7 + (0.000217013888888889) * x^9"
##
## $order
## [1] 9
##
## $terms
## var coef degree
## 0 1 0.0000000000 0
## 1 x^1 0.5000000000 1
## 2 x^2 0.0000000000 2
## 3 x^3 -0.0416666667 3
## 4 x^4 0.0000000000 4
## 5 x^5 0.0062500000 5
## 6 x^6 0.0000000000 6
## 7 x^7 -0.0011160714 7
## 8 x^8 0.0000000000 8
## 9 x^9 0.0002170139 9