Matematika

Pertanyaan

Bagi-bagi poin, please bantuin dong, pake jalan kerjanya juga ya
Bagi-bagi poin,  please bantuin dong, pake jalan kerjanya juga ya

1 Jawaban

  • 1) Un = 4ⁿ
        U2 = 4² = 16
        U1 = 4¹ = 4

        r = U2/U1
          = 16/4
          = 4

        Un = a rⁿ⁻¹
         4ⁿ = 4 (4)ⁿ⁻¹
         4ⁿ = 4²⁽ⁿ⁻¹⁾
         n = 2(n - 1)
         n = 2n - 1
         1 = 2n - n
         1 = n
    S1 = U1 = 4

    2)        (3x - 2)¹/²  -  (2x + 4)¹/²             (3)1/2(3x - 2)⁻¹/² - (2)1/2(2x + 4)⁻¹/²
        lim  ------------------------------- =  lim  ------------------------------------------------
        ₓ→₆             x - 6                      ˣ→₆                           1

                                                     =  3/2 (3(6) - 2)⁻¹/² - (2(6) + 4)⁻¹/²
                                                     =  3/2 (4²)⁻¹/²  -  (4²)⁻¹/²
                                                     =  3/2 (1/4) - (1/4)
                                                     = 3/8 - 2/8
                                                     = 1/8

    3)  lim (3x -2) - √(9x² - 2x + 5)  = lim  √(3x -2)² - √(9x² - 2x + 5)
      ˣ→∞                                           ˣ→∞
                                                     = lim   √(9x² -12x + 4) - √(9x² - 2x + 5)
                                                        ˣ→∞
        a = 9
        b = -12
        q = - 2
                                                         b - q
                                                      = -------
                                                          2√a
                                                          -12 -(-2)
                                                      = -------------
                                                             2√9
                                           
                                                            - 10
                                                       = -----------
                                                             2(3)
                                                       = - 10/6
                                                       = - 5/3