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# ===============================================================
# SOAL 1a
# Menghitung nilai eksponensial exp(x) dengan deret Maclaurin
# Rumus:
# exp(x) = 1 + x + x^2/2! + x^3/3! + ... + x^n/n!
# Fungsi menerima input x dan n (orde deret)
# ===============================================================

faktorial_manual <- function(n){
  hasil <- 1
  
  if(n == 0){
    hasil <- 1
  } else {
    for(i in 1:n){
      hasil <- hasil * i
    }
  }
  
  return(hasil)
}

exp_maclaurin <- function(x, n){
  total <- 0
  
  for(i in 0:n){
    suku_ke_i <- (x^i) / faktorial_manual(i)
    total <- total + suku_ke_i
  }
  
  return(total)
}


hasil_exp <- exp_maclaurin(-1, 5)
print(hasil_exp)

## [1] 0.3666667

# ===============================================================
# SOAL 1b
# Menghitung nilai sin(x) dengan deret Maclaurin
# Rumus:
# sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
# Perhitungan berhenti jika suku terakhir berada di antara
# -10^-5 dan 10^-5
# ===============================================================

sin_maclaurin <- function(x){
  hasil <- 0
  
  for(i in 0:100){
    
    suku <- ((-1)^i) * (x^(2*i + 1)) / faktorial_manual(2*i + 1)
    
    if(suku < 10^-5 & suku > -10^-5){
      break
    }
    
    hasil <- hasil + suku
  }
  
  return(hasil)
}

hasil_sin <- sin_maclaurin(pi/6)
print(hasil_sin)

## [1] 0.5000021

sin(pi/6)

## [1] 0.5

# ===============================================================
# SOAL 2
# Menghitung rata-rata bergerak M_t(k)
# Rumus:
# M_t(k) = (Y_t + Y_(t-1) + ... + Y_(t-k+1)) / k
# Pada soal digunakan k = 3
# ===============================================================

data_nilai <- c(4.1, 4.9, 6.2, 6.9, 6.8, 4.4, 5.7, 5.8, 6.9, 4.7, 6.0, 4.9)

moving_average <- function(data, k){
  n <- length(data)
  hasil <- c()
  
  for(i in k:n){
    jumlah <- 0
    
    for(j in (i-k+1):i){
      jumlah <- jumlah + data[j]
    }
    
    rata_rata <- jumlah / k
    hasil <- c(hasil, rata_rata)
  }
  
  return(hasil)
}

hasil_mt3 <- moving_average(data_nilai, 3)

round(hasil_mt3, 2)

##  [1] 5.07 6.00 6.63 6.03 5.63 5.30 6.13 5.80 5.87 5.20