Nilai dari lim x → 0 sin2x - tan2x / x³ adalah?
Matematika
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Pertanyaan
Nilai dari lim x → 0 sin2x - tan2x / x³ adalah?
1 Jawaban
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1. Jawaban arsetpopeye
Lim (sin 2x - Tan 2x)/x^3
= Lim (sin 2x - (sin 2x)/(cos 2x)) / x^3 . (cos 2x)/(cos 2x)
= Lim (sin 2x cos 2x - sin 2x) / (cos 2x . x^3)
= Lim sin 2x (cos 2x - 1) / (cos 2x . x^3)
= Lim sin 2x . -2 sin^2 x / (cos 2x . x^3)
= Lim -2/(cos 2x) . (sin 2x)/x . (sin x)/x . (sin x)/x
= -2/(cos 2.0) . 2/1 . 1 . 1
= -2/(cos 0) . 2
= -2/1 . 2
= -4