Taylor Series e^x GIF

library(tidyverse)
library(MASS)

# plot e^x
x <- -5:5
dat <- data.frame(x,y=exp(x))

f <- function(x) exp(x)
p <- ggplot(dat, aes(x,y)) +
  stat_function(fun=f, colour="red") +
  theme_minimal() +
  labs(title = "e^x")  +
  ylim(c(0,150))

# plot taylor polynomials

# 0
f <- function(x) 1

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 0-degree Taylor Polynomial")


# 1
f <- function(x) 1  + x

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 1-degree Taylor Polynomial")

# 2
f <- function(x) 1  + x + (x**2)/factorial(2)

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 2-degree Taylor Polynomial")

# 3
f <- function(x) 1  + x + (x**2)/factorial(2) + (x**3)/factorial(3)

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 3-degree Taylor Polynomial")


# 4
f <- function(x) 1  + x + (x**2)/factorial(2) + (x**3)/factorial(3) +
  (x**4)/factorial(4)

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 4-degree Taylor Polynomial")


# 5
f <- function(x) 1  + x + (x**2)/factorial(2) + (x**3)/factorial(3) +
  (x**4)/factorial(4) + (x**5)/factorial(5)

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 5-degree Taylor Polynomial")


# 6
f <- function(x) 1  + x + (x**2)/factorial(2) + (x**3)/factorial(3) +
  (x**4)/factorial(4) + (x**5)/factorial(5) + (x**6)/factorial(6) 

p + stat_function(fun = f, color = "blue") +
  labs(title = "e^x approximated by a 6-degree Taylor Polynomial")


# background image

ggplot(dat, aes(x,y)) +
  theme_void() 
  ylim(c(0,150))
ggsave(paste0(home, "background.png"),
       height = 4, width = 6, units = "in", bg = "white")