Universitas :“UIN MAULANA MALIK IBRAHIM MALANG”

Jurusan : “Teknik Informatika”

Penyelesaian Soal Pertidaksamaan

1. 4x - 7 < 3x - 5

Jawab

4x-7<3x-5

4 x - 3 x < 7 -5

x < 2

root_table <- function(f, a, b, N=20){
    h <- abs((a+b)/N)
    x <- seq(from=a, to=b, by=h)
    fx <- rep(0, N+1)
    for(i in 1:(N+1)){
      fx[i] <- f(x[i])
    }
    data <- data.frame(x=x, fx=fx)
    return(data)
}
tabel <- root_table(f=function(x){4*x-7<3*x-5},
                     a=0, b=2, N=10)
print(tabel)
##      x fx
## 1  0.0  1
## 2  0.2  1
## 3  0.4  1
## 4  0.6  1
## 5  0.8  1
## 6  1.0  1
## 7  1.2  1
## 8  1.4  1
## 9  1.6  1
## 10 1.8  1
## 11 2.0  0
# membuat vektor data 
x <- c(0:2); y <- 4*x-7<3*x-5
# membagi jendela grafik menajdi 1 baris dan 1 kolom
par(mfrow=c(1,1))

# loop
type <- c("p","l","b","o","h","s","n")
for (i in type){
  plot(x, y, type="l")
}

2. 2x – 4 ≤ 6 – 7x ≤ 3x + 6

Jawab

2x – 4 ≤ 6 – 7x ≤ 3x + 6

6-7x >= 2x-4 6-7x <= 3x +6

-7x-2x >= -4-6 -7x-3x <= 6-6

-9x >= -10 -10x <= 0

x <= 10/9 x >= 0

jadi Hp nya : 0 <= x <= 10/9 atau Hp nya : 0 <= x <= 1.11

root_table <- function(f, a, b, N=20){
    h <- abs((a+b)/N)
    x <- seq(from=a, to=b, by=h)
    fx <- rep(0, N+1)
    for(i in 1:(N+1)){
      fx[i] <- f(x[i])
    }
    data <- data.frame(x=x, fx=fx)
    return(data)
}
tabel <- root_table(f=function(x){2*x - 4 -6+7*x+3*x +6},
                     a=0, b=1.99, N=10)
print(tabel)
##        x     fx
## 1  0.000 -4.000
## 2  0.199 -1.612
## 3  0.398  0.776
## 4  0.597  3.164
## 5  0.796  5.552
## 6  0.995  7.940
## 7  1.194 10.328
## 8  1.393 12.716
## 9  1.592 15.104
## 10 1.791 17.492
## 11 1.990 19.880
# membuat vektor data 
x <- c(1.99:0); y <- 2*x - 4 -6+7*x+3*x +6
# membagi jendela grafik menajdi 1 baris dan 1 kolom
par(mfrow=c(1,1))

# loop
type <- c("p","l","b","o","h","s","n")
for (i in type){
  plot(x, y, type="l")
}

3. x^2 + x – 12 < 0

jawab

1* x^2 + 1*x – 12

(x+4) (x-3)

x < -4 atau x < 3

jadi Hp nya : x < -4 dan x < 3

root_table <- function(f, a, b, N=20){
    h <- abs((a+b)/N)
    x <- seq(from=a, to=b, by=h)
    fx <- rep(0, N+1)
    for(i in 1:(N+1)){
      fx[i] <- f(x[i])
    }
    data <- data.frame(x=x, fx=fx)
    return(data)
}
tabel <- root_table(f=function(x){1*x^2+1*x - -12},
                     a=-4, b=0, N=10)
print(tabel)
##       x    fx
## 1  -4.0 24.00
## 2  -3.6 21.36
## 3  -3.2 19.04
## 4  -2.8 17.04
## 5  -2.4 15.36
## 6  -2.0 14.00
## 7  -1.6 12.96
## 8  -1.2 12.24
## 9  -0.8 11.84
## 10 -0.4 11.76
## 11  0.0 12.00
# membuat vektor data 
x <- c(-4:3); y <- 1*x^2+1*x - -12
# membagi jendela grafik menajdi 1 baris dan 1 kolom
par(mfrow=c(1,1))

# loop
type <- c("p","l","b","o","h","s","n")
for (i in type){
  plot(x, y, type="l")
}

4.3x2 - 11x - 4 <=0

jawab

3* x^2 - 11 *x - 4

(3x-1) (x-4)

3x <= -1 atau X <= 4

root_table <- function(f, a, b, N=20){
    h <- abs((a+b)/N)
    x <- seq(from=a, to=b, by=h)
    fx <- rep(0, N+1)
    for(i in 1:(N+1)){
      fx[i] <- f(x[i])
    }
    data <- data.frame(x=x, fx=fx)
    return(data)
}
tabel <- root_table(f=function(x){3*x^2 - 11*x - 4},
                     a=0, b=4, N=10)
print(tabel)
##      x     fx
## 1  0.0  -4.00
## 2  0.4  -7.92
## 3  0.8 -10.88
## 4  1.2 -12.88
## 5  1.6 -13.92
## 6  2.0 -14.00
## 7  2.4 -13.12
## 8  2.8 -11.28
## 9  3.2  -8.48
## 10 3.6  -4.72
## 11 4.0   0.00
# membuat vektor data 
x <- c(-1:4); y <- 3*x^2 - 11*x - 4
# membagi jendela grafik menajdi 1 baris dan 1 kolom
par(mfrow=c(1,1))

# loop
type <- c("p","l","b","o","h","s","n")
for (i in type){
  plot(x, y, type="l")
}

x+5/2x-1 <= 0

jawab

1* x+5/ 2 *x-1

x+5 <= 0 dan 2x-1 <0

x >= -5 dan X < 1/2

root_table <- function(f, a, b, N=20){
    h <- abs((a+b)/N)
    x <- seq(from=a, to=b, by=h)
    fx <- rep(0, N+1)
    for(i in 1:(N+1)){
      fx[i] <- f(x[i])
    }
    data <- data.frame(x=x, fx=fx)
    return(data)
}
tabel <- root_table(f=function(x){1*x +5/ 2*x-1},
                     a=-5, b=0, N=10)
print(tabel)
##       x     fx
## 1  -5.0 -18.50
## 2  -4.5 -16.75
## 3  -4.0 -15.00
## 4  -3.5 -13.25
## 5  -3.0 -11.50
## 6  -2.5  -9.75
## 7  -2.0  -8.00
## 8  -1.5  -6.25
## 9  -1.0  -4.50
## 10 -0.5  -2.75
## 11  0.0  -1.00
# membuat vektor data 
x <- c(-5:0.5); y <- 1*x +5/ 2*x-1
# membagi jendela grafik menajdi 1 baris dan 1 kolom
par(mfrow=c(1,1))

# loop
type <- c("p","l","b","o","h","s","n")
for (i in type){
  plot(x, y, type="l")
}

REFERENSI

https://bookdown.org/moh_rosidi2610/Metode_Numerik/diffinteg.html#diferensiasi-metode-titik-pusat-mengggunakan-fungsidiff

Suhartono.2015.Memahami Kalkulus Dasar Menggunakan Wolfram Mathematica 9.UIN Maliki Malang: Malang.