lim (x→0)(cos 8x-cos 2x)/(4x sin x)=...

Jawaban : -15/2 Halo Nadya, kakak bantu jawab ya Ingat cos A - cos B = -2 sin((A+B)/2) sin((A-B)/2) Lim_(x→0) sin ax/ sin bx = a/b Lim_(x→0) sin ax/ bx = a/b Sehingga lim (x→0)(cos 8x-cos 2x)/(4x sin x) = lim (x→0)(-2 sin((8x+2x)/2) sin((8x-2x)/2))/(4x sin x) = -2 lim (x→0)(sin5x sin3x)/(4x sin x) = -2 lim (x→0)(sin5x)/(4x) lim (x→0) (sin3x)/(sin x) = -2∙5/4∙3 = -15/2 Jadi, nilai limit diatas adalah -15/2.