Matematika

Pertanyaan

Lim x menuju 0 cosx-cos 3x per 1-cos 2x .......

2 Jawaban

  • (cos x - cos 3x) / (1 - cos 2x)
    = (-2.sin 2x sin -x) / (1 - (1 - sin²x))
    = (-2.sin 2x sin -x) / (1 - 1 + sin²x)
    = (-2.sin 2x sin -x) / (sin x sin x)
    = -2.(2).(-1)
    = 4
  • Lim (cos x - cos 3x) / (1 - cos 2x)
    = Lim (-2 sin (x + 3x)/2 sin (x - 3x)/2) / (2 sin^2 x)
    = Lim (-2 sin 2x sin (-x)) / (2 sin^2 x)
    = Lim -2/2 . (sin 2x)/(sin x) . (sin (-x))/(sin x)
    = -1 . 2/1 . -1/1
    = 2

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