Tugas 3_Adinda Najwa Naiza

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#01
  exp_maclaurin <- function(x, n){
    hasil <- 0
    for(k in 0:n){
      hasil <- hasil + (x^k)/factorial(k)
    }
    return(hasil)
  }
  
  # Contoh:
  exp_maclaurin(-1, 5)

[1] 0.3666667

  
  sin_maclaurin <- function(x){
    hasil <- 0
    k <- 0
    suku <- x  # suku pertama
    
    while(abs(suku) >= 1e-5){
      hasil <- hasil + suku
      k <- k + 1
      suku <- (-1)^k * x^(2*k+1) / factorial(2*k+1)
    }
    
    return(hasil)
  }
  
  # Contoh:
  sin_maclaurin(pi/6)

[1] 0.5000021

  
  sin_detail <- function(x){
    k <- 0
    
    repeat{
      suku <- ((-1)^k) * x^(2*k + 1) / factorial(2*k + 1)
      
      cat("Suku ke-", k, ":", suku, "\n")
      
      if(abs(suku) < 1e-5){
        break
      }
      
      k <- k + 1
    }
  }
  
  # Jalankan:
  sin_detail(pi/6)

Suku ke- 0 : 0.5235988 
Suku ke- 1 : -0.0239246 
Suku ke- 2 : 0.0003279532 
Suku ke- 3 : -2.14072e-06 

  
#02
  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)
  
  moving_average <- function(data, k){
    n <- length(data)
    hasil <- rep(NA, n)
    
    for(t in k:n){
      hasil[t] <- mean(data[(t-k+1):t])
    }
    
    return(hasil)
  }
  
  Mt3 <- moving_average(data, 3)
  
  hasil <- data.frame(
    t = 1:length(data),
    Data = data,
    Mt3 = round(Mt3, 2)
  )
  
  print(hasil)

    t Data  Mt3
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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