[tex] \lim_{x \to \ \frac{ \pi }{3} \frac{1 - 2 cos x}{ \pi - 3x} [/tex]

Dengan cara L'HOSPITAL (turunan)
Lim (1 - 2 cos x)/(π - 3x)
x=>π/3

Lim (2 sin x) / -3
x=>π/3

= (2 sin π/3) / -3
= (2 . 1/2 √3) / -3
= -1/3 √3

Cara biasa :
Lim (1 - 2 cos x) / (π - 3x)
x=>π/3

Lim (1 - 2 cos x)/(π - 3x) . (1 + 2 cos x)/(1 + 2 cos x)
x=>π/3

Lim (1 - 4 cos^2 x) / (π - 3x)(1 + 2 cos x)
x=>π/3

Lim ((sin^2 x + cos^2 x) - 4 cos^2 x) / (π - 3x)/(1 + 2 cos x)
x=>π/3

Lim (sin^2 x - 3 cos^2 x) / (π - 3x)(1 + 2 cos x)
x=>π/3

Lim (sin x - √3 cos x)(sin x + √3 cos x) / (π - 3x)(1 + 2 cos x)
x=>π/3

Lim (2 sin (x - π/3)) (sin x + √3 cos x) / -3(x - π/3)(1 + 2 cos x)
x=>π/3

Lim (2/-3) . (sin (x - π/3))/(x - π/3) . (sin x + √3 cos x)/(1 + 2 cos x)
x=>π/3

= -2/3 . 1 . (sin π/3 + √3 cos π/3)/(1 + 2 cos π/3)
= -2/3 . (1/2 √3 + 1/2 √3) / (1 + 2(1/2))
= -2/3 . (√3/2)
= -1/3 √3