Matematika

Pertanyaan

ada yang bisa bantu saya kah?soal limit trigonometri..trimakasih sebelumnya
ada yang bisa bantu saya kah?soal limit trigonometri..trimakasih sebelumnya

1 Jawaban

  • 8) Lim (1 - cos x)/(3x sin x)
    = Lim (2 sin^2 1/2 x)/(3x sin x)
    = Lim 2 . (sin 1/2 x)/(3x) . (sin 1/2 x)/(sin x)
    = 2 . (1/2)/3 . (1/2)/1
    = 1/6

    9) Lim sec x (Tan x - sin x)/x
    = Lim 1/(cos x) . ((Tan x)/x - (sin x)/x)
    = 1/(cos 0) . (1/1 - 1/1)
    = 1/1 (0)
    = 0

    10) Lim (sin 3x - sin 3x cos 2x)/(8x^2)
    = Lim sin 3x (1 - cos 2x)/(8x^2)
    = Lim (sin 3x . 2 sin^2 x)/(8x^2)
    = Lim (sin 3x)/8 . 2 . (sin x)/x . (sin x)/x
    = (sin 0)/8 . 2 . 1 . 1
    = 0/8 . 2
    = 0

    7) Lim (1 - Tan x) sec 2x
    = Lim (1 - Tan x) . 1/(cos 2x)
    = (1 - Tan π/2) . 1/(cos π)
    = (1 - ~) . 1/(-1)
    = -~ . -1
    = ~