Lim x-0 cos 8x -1/x sin 4x

cos 8x = cos(4x+4x) = cos4x cos4x - sin4 sin4x = cos^2 4x - sin^2 4x

jawab

limit (x->0) ( cos 8x - 1) / ( x. sin 4x)

lim(x->0)  (1 - 2 sin² 4x - 1) / (x sin 4x)

lim(x->0)  ( - 2 sin² 4x) / (x sin 4x)

= - 2 (4)²/ (1)(4)
= -8