Tentutan nilai limit fungsi trigonometri berikut. a.) lim_(x --->3)(x tan(2x-6))/(sin(x-3))

Jawaban yang benar adalah 6 Pembahasan Ingat! 1. tan α = sin α / cos α 2. sin 2α = 2 sin α cos α 3. cos 2α = 2cos² α – 1 4. Lim (x → c) f(x) = f(c) lim(x → 3) (x tan (2x – 6))/(sin (x – 3)) = (3 . tan (2(3) – 6))/sin (3 – 3) = (3 . tan (6 – 6))/sin 0 = (3 . tan 0)/sin 0 = (3 . 0) / 0 = 0/0 (bentuk tak tentu) lim(x → 3) (x tan (2x – 6))/(sin (x – 3)) = lim(x → 3) (x (sin (2x – 6) / cos (2x – 6))/(sin (x – 3)) = lim(x → 3) (x sin 2(x – 3) / cos 2(x – 3)) . 1/(sin (x – 3)) = lim(x → 3) (x . 2 sin (x – 3) cos (x – 3)) / (cos 2(x – 3))(sin (x – 3)) = lim(x → 3) (2x cos (x – 3)) / (cos 2(x – 3)) = lim(x → 3) (2x cos (x – 3)) / (2 cos²(x – 3) – 1) = (2(3) cos (3 – 3)) / (2 cos²(3 – 3) – 1) = (6 cos 0) / (2 cos²0 – 1) = (6 . 1) / (2 . 1 – 1) = 6/1 = 6 Jadi, nilai dari lim(x → 3) (x tan (2x – 6))/(sin (x – 3)) adalah 6