Assigment 3

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# 1.  Eksponensial 

exp_maclaurin <- function(x, n) {
  hasil <- 0
  
  for (i in 0:n) {
    hasil <- hasil + (x^i) / factorial(i)
  }

  return(hasil)
}
x1 <- -1
n1 <- 5
hasil_exp <- exp_maclaurin(x1, n1)
print(hasil_exp)

## [1] 0.3666667

#sin maclaurin
sin_maclaurin <- function(x, tol = 1e-5) {
  hasil <- 0
  i <- 0
  term <- x
  
  while (abs(term) > tol) {
    term <- ((-1)^i * x^(2*i + 1)) / factorial(2*i + 1)
    hasil <- hasil + term
    i <- i + 1
  }
  
  return(hasil)
}

x2 <- pi/6
hasil_sin <- sin_maclaurin(x2)
print(hasil_sin)

## [1] 0.5

# rata rata bergerak
moving_average <- function(data, k) {
  n <- length(data)
  hasil <- rep(NA, n)  # supaya panjang sama dengan data
  
  for (i in k:n) {
    hasil[i] <- mean(data[(i-k+1):i])
  }
  
  return(hasil)
}

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

k <- 3

M3 <- moving_average(data, k)

t <- 1:length(data)

hasil <- data.frame(
  t = t,
  Data = data,
  M3 = round(M3, 2)
)

print(hasil)

##     t Data   M3
## 1   1  4.1   NA
## 2   2  4.9   NA
## 3   3  6.2 5.07
## 4   4  6.9 6.00
## 5   5  6.8 6.63
## 6   6  4.4 6.03
## 7   7  5.7 5.63
## 8   8  5.8 5.30
## 9   9  6.9 6.13
## 10 10  4.7 5.80
## 11 11  6.0 5.87
## 12 12  4.9 5.20

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