Nama: Muhammad Sharqarchie Bayanaka NRP: 5003251098 Kelas: D Departemen: Statistika

#1a)

mclaurin_function = function(x, n){
  sum = 0
  for(i in 0:n){
    sum = sum + (x^i)/factorial(i)
  }
  return(sum)
}

mclaurin_function(-1, 5)

## [1] 0.3666667

#1b)

sin_function = function(x){
  sum = 0
  i = 1
  simbol = 1
  rumus = x^i/factorial(i)
  
  while(abs(rumus)>=10^-5){
    sum = sum + simbol * rumus
    simbol = -simbol
    i = i+2
    rumus = x^i/factorial(i)
  }
  return(sum)
}
sin_function(pi/6)

## [1] 0.5000021

#2)

mean_function = function(data){
  n = length(data)
  sum = 0
  
  for(i in 1:n){
    sum = sum + data[i]
  }
  return(sum/n)
}

mean_bergerak = function(data, k){
  n = length(data)
  hasil = rep(NA, n)
  
  for(t in k:n){
    hasil[t] = mean_function(data[(t-k+1):t])
  }
  return(hasil)
}

data = c(4.1, 4.9, 6.2, 6.9, 6.8, 4.4, 5.7, 5.8, 6.9, 4.7, 6, 4.9)
Mt = mean_bergerak(data, 3)

tabel_df = data.frame(
  t = 1:length(data),
  Data = data,
  Mt_3 = Mt
)
print(tabel_df)

##     t Data     Mt_3
## 1   1  4.1       NA
## 2   2  4.9       NA
## 3   3  6.2 5.066667
## 4   4  6.9 6.000000
## 5   5  6.8 6.633333
## 6   6  4.4 6.033333
## 7   7  5.7 5.633333
## 8   8  5.8 5.300000
## 9   9  6.9 6.133333
## 10 10  4.7 5.800000
## 11 11  6.0 5.866667
## 12 12  4.9 5.200000