LImitTrigonometri
Penjelasan dengan langkah-langkah:
Limit 0/0
L'Hopital
π/6 = 180°/6 = 30°
lim x→π/6 (sin 4x - sin 2x)/(cos 4x + cos 2x)
= lim x→30° (4 cos 4x - 2 cos 2x) / (-4 sin 4x - 2 sin 2x)
= (2 cos 120° - cos 60°) / (-2 sin 120° - sin 60°)
= (-2(1/2) - 1/2) / (-2(1/2 √3) - 1/2 √3)
= (-3/2) / (-3/2 √3)
= 1/√3
= 1/3 √3
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LImit
Trigonometri
Penjelasan dengan langkah-langkah:
Limit 0/0
L'Hopital
π/6 = 180°/6 = 30°
lim x→π/6 (sin 4x - sin 2x)/(cos 4x + cos 2x)
= lim x→30° (4 cos 4x - 2 cos 2x) / (-4 sin 4x - 2 sin 2x)
= (2 cos 120° - cos 60°) / (-2 sin 120° - sin 60°)
= (-2(1/2) - 1/2) / (-2(1/2 √3) - 1/2 √3)
= (-3/2) / (-3/2 √3)
= 1/√3
= 1/3 √3