# Taylor series illustration
x <- seq(0.01, 3, len=199)
plot(x, log(x), col="gray", lwd=3, type="l", ylab="f(x)", las=1, bty='n')
lines(x, x-1, lwd=3, col='#FF4E37')
points(1, 0, pch=19, col='black')
lines(x, (x - 1) - (1/2) * (x-1)^2, lwd=3, col='#008DFF')
lines(x, (x - 1) - (1/2) * (x-1)^2 + (1/2) * (x-1)^3, lwd=3, col='#00B500')