Tugas 3

Alfarrel Mahendra L. | 5003251034

1. a

faktorial <- function(x){
  fakt <- 1
  if(x <= 0){
    return(1)
  }else{
    for(i in 1:x){
      fakt <- fakt*i
    }
    return(fakt)
  }
}
eksponensial <- function(x, n){
  sum <- 1
  for(i in 1:n){
    sum <- sum + x^i/faktorial(i)
  }
  return(sum)
}

eksponensial(-1, 5)

[1] 0.3666667

1.b

sin_function <- function(x){
  sum <- x
  i <-  1
  suku  <- 1

  while(suku > 10^(-5)){
    pembilang <- x^(2*i + 1)
    penyebut <- faktorial(2*i + 1)
    suku <- pembilang/penyebut 
    sum <-  sum + (-1)^i * suku
    
    i = i+1
  }
  return(sum)
}

sin_function(pi/6)

[1] 0.5

2

mean_data <- function(x){
  n <- length(x)
  sumx <- 0
  for(i in 1:n){
    sumx = sumx + x[i]
  }
  return(sumx/n)
}

rata2_bergerak <- function(x, k = 3) {
  n <- length(x)
  Mt <- rep(NA, n)  
  for (t in k:n) {
    Mt[t] <- mean_data(x[(t-k+1):t])
  }
  return(Mt)
}

data <- 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)

Mt3 <- rata2_bergerak(data, 3)