Part I Chapter 2

options(scipen = 7)

13쪽 설명

x <- c(1.0, 1.5, 1.8, 1.9, 1.95, 1.99, 1.995, 1.999, 3.0, 2.5, 2.2, 2.1, 2.05, 2.01, 2.005, 2.001)
y <- x^2 - x + 2
curve(x^2 - x + 2, -4, 4)

plot(x, y, pch = 20)

plot(x, y, xlim = c(1.5, 2.5), ylim = c(2, 6), pch = 20)

plot(x, y, xlim = c(1.8, 2.2), ylim = c(3, 5), pch = 20)

plot(x, y, xlim = c(1.9, 2.1), ylim = c(3.5, 4.5), pch = 20)

예제 1

x <- c(0.5, 0.9, 0.99, 0.999, 0.9999)
y <- (x - 1)/(x^2 - 1)
curve((x - 1)/(x^2 - 1), -2, 2, ylim = c(-10, 10))
points(1, 0.5)

curve((x - 1)/(x^2 - 1), -2, 2, ylim = c(-10, 10))
points(1, 0.5)
points(1, 2, pch = 20)

예제 2

x <- c(-1., -0.5, -0.1, -0.05, -0.01, -0.0005, -0.0001, -0.00005, -0.00001, 0.00001, 0.00005, 0.0001, 0.0005, 0.01, 0.05, 0.1, 0.5, 1.)
y <- (sqrt(x^2 + 9) - 3)/x^2
cbind(x, y)

##              x         y
##  [1,] -1.00000 0.1622777
##  [2,] -0.50000 0.1655251
##  [3,] -0.10000 0.1666204
##  [4,] -0.05000 0.1666551
##  [5,] -0.01000 0.1666662
##  [6,] -0.00050 0.1666667
##  [7,] -0.00010 0.1666667
##  [8,] -0.00005 0.1666667
##  [9,] -0.00001 0.1666667
## [10,]  0.00001 0.1666667
## [11,]  0.00005 0.1666667
## [12,]  0.00010 0.1666667
## [13,]  0.00050 0.1666667
## [14,]  0.01000 0.1666662
## [15,]  0.05000 0.1666551
## [16,]  0.10000 0.1666204
## [17,]  0.50000 0.1655251
## [18,]  1.00000 0.1622777

plot(x, y, pch = 20)

curve((sqrt(x^2 + 9) - 3)/x^2, -2, 2)
points(0, 1/6)

2.1-15

x <- seq(0.01, 10, length = 100)
y <- (1 + x)^(1/x)
curve((1 + x)^(1/x), 0.00001, 5)

plot(x, y, pch = 20)

2.2-11

curve(x/(x^2 + 5*x + 6), -5, 0)
abline(v = c(-3, -2), h = 0, lty = 2)

2.3-16

curve(x/(sqrt(1 + 3*x) - 1), -1/3, 2)

curve((sqrt(1 + 3*x) + 1)/3, -1/3, 2)