lim x mendekati 0 dari 4x/{cot x(cos x-1)} adalah???? Terimakasih sudah membantu :)

Lim (4x)/(cot x (cos x - 1))
x=>0

Lim (4x tan x) / -(1 - cos x)
x=>0

Lim (4x tan x) / -(2 sin² 1/2 x)
x=>0

Lim 1/-2 . (4x)/(sin 1/2 x) . (tan x)/(sin 1/2 x)
x=>0

= -1/2 . 4/(1/2) . 1/(1/2)

= -1/2 . 8 . 2

= -8

LImit trigonomteri
cot x = 1/tan x
cos x - 1 = -2 sin² 1/2 x
.
cot x (cos x -1) = (1/tan x) ( - 2 sin² 1/2 x) = - 2 sin² 1/2 x / tan x
.
limit (x- 0)  4x / { cot x (cos x-1)} =
= limit (x->0)  4x /{-2 sin² 1/2 x / tan x}
= limit (x-> 0)  (4x. tan x) /(-2 sin² 1/2 x)
x= 0
limit = 4x (x) / (-2)(1/2 x)² = 4x² /(- 1/2 x²) = - 8