Question

Lim x--0 sinx/ x = 1
Maka lim x--0 cos x- cos 2x / x^2

Answer 1

Lim (x->0) { cos x - cos 2x) / (x^2)
lim (x->0) { - 2 sin 1/2(x + 2x) . sin 1/2( x - 2x) / (x^2)
lim (x->0) = { - 2 sin 3/2 x . sin -1/2 x)/(x^2)
= -2 (3/2 x)(-1/2 x) / (x^2)
= 3/2