nilai lim x->2 1-cos2(x-2) : x^2-4x+4 sama dengan
Matematika
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Pertanyaan
nilai lim x->2 1-cos2(x-2) : x^2-4x+4 sama dengan
2 Jawaban
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1. Jawaban DimasRaka
(1 - cos²(x - 2)) / (x² - 4x + 4)
= sin²(x - 2) / (x - 2)²
= 1 -
2. Jawaban arsetpopeye
Lim (1 - cos 2(x - 2)) / (x^2 - 4x + 4)
= Lim (1 - (1 - 2 sin^2 (x - 2)) / (x - 2)(x - 2)
= Lim (2 sin (x - 2) sin (x - 2)) / (x - 2)(x - 2)
= Lim 2 . (sin (x - 2))/(x - 2) . (sin (x - 2))/(x - 2)
= 2 . 1 . 1
= 2