Assignment 3

Identitas

Nama : Ismanda Felisa Clearance Abdullah
NRP : 5003251116
Kelas : D

Soal 1a

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

exp_maclaurin(-1, 5)

## [1] 0.3666667

#Soal 1b

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)
}

sin_maclaurin(pi/6)

## [1] 0.5

Soal 2

t <- 1:12

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)

df <- data.frame(t, data)
df

moving_average <- function(data, k) {
  n <- length(data)
  hasil <- rep(NA, n)
  
  for (i in k:n) {
    hasil[i] <- mean(data[(i-k+1):i])
  }
  
  return(hasil)
}

df$Mt_3 <- moving_average(df$data, 3)
df