lim_(x→0) (1−cos 8x)/(sin 2x ⋅ tan 2x) = ....

Jawaban yang benar adalah 4 Ingat kembali, lim x->0 sin ax/bx = a/b lim x->0 sin ax/tan bx = a/b cos nx = 1 - 2 sin² (n/2)x sin 2x = 2 sin x cos x lim_(x→a) f(x) = a Berdasarkan sifat di atas, maka diperoleh lim_(x→0) (1−cos 8x)/(sin 2x ⋅ tan 2x) = lim_(x→0) (1− (1 - sin ² 4x))/(sin 2x ⋅ tan 2x) = lim_(x→0) (1− 1 + sin ² 4x))/(sin 2x ⋅ tan 2x) = lim_(x→0) (sin ² 4x))/(sin 2x ⋅ tan 2x) = lim_(x→0) (sin 4x)/(sin 2x )⋅ lim_(x→0) (sin 4x)/(tan 2x) = lim_(x→0) (2 .sin 2x . cos 2x)/(sin 2x )⋅ 4/2 = lim_(x→0) (2 cos 2x) . 2 = 2 . 1 . 2 = 4 Dengan demikian, hasil dari lim_(x→0) (1−cos 8x)/(sin 2x ⋅ tan 2x) adalah 4.