lim(x -> 0) [(2tan² 3x . sin 2x)/(4x² sin 6x)]

Jawaban: 3/2 Konsep: Limit Trigonometri lim(x → 0) (tan ax)/bx = a/b lim(x → 0) (sin ax)/(sin bx) = a/b Pembahasan lim(x → 0) [(2tan² 3x . sin 2x)/(4x² sin 6x)] = lim(x → 0) [(2.(tan3x)² . sin 2x)/((2x)² sin 6x)] = lim(x → 0) [(2.tan3x.tan3x . sin 2x)/(2x.2x. sin 6x)] = lim(x → 0) [(2.tan3x/2x). (tan3x/2x) . (sin 2x/sin 6x)] = lim(x → 0) [(2.tan3x/2x)]. lim(x → 0) [(tan3x/2x)] . lim(x → 0) [(sin 2x/sin 6x)] = 2.3/2 . 3/2 . 2/6 = 3 . 3/2 .1/3 = (3.3.1)/(2.3) = 3/2 Jadi, jawabannya adalah 3/2.