Matematika

Pertanyaan

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1 Jawaban

  • Bab Differensial dan Limit
    Matematika SMA Kelas XI

    2] f(x) = 4 sin x cos x
    f(x) = 2 . (2 . sin x cos x)
    f(x) = 2 . sin 2x
    f'(x) = 2 . cos 2x . 2
    f''(x) = 4 . (-sin 2x) . 2
    f"(x) = -8 sin 2x

    jawabannya E

    3] lim ((1 - cos 2x)/x²)
       x→0
    = lim ((1 - (1 - 2 sin² x))/x²)
      x→0
    = lim ((2 sin² x)/x²)
       x→0
    = 2

    jawabannya E

    4] lim ((9 - x)/(x² - 9) - (1/(x - 3)))
       x→3

    = lim ((9 - x - x - 3)/(x² - 9))
      x→3

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

    = lim (2 (3 - x) / (- (3 - x) (x + 3))
      x→3

    = 2/(-(3 + 3))
    = 2/-6
    = -1/3

    jawabannya D