[tex] \lim_{x \to 0} \frac{ x^{2} \sqrt{4-x} }{cosx-cos3x} [/tex] a. -2 b. -1/2 c. 1/2 d. 1 e. 2

Lim x^2 √(4 - x) / (cos x - cos 3x)
= Lim √(4 - x) . x^2 / (-2 sin (x+3x)/2 sin (x-3x)/2)
= Lim √(4 - x) . x^2 / (-2 sin 2x sin (-x))
= Lim √(4 - x) . x.x / (2 sin 2x sin x)
= Lim (√(4 - x))/2 . x/(sin 2x) . x/(sin x)
= (√(4 - 0)) / 2 . 1/2 . 1/1
= 1 . 1/2 . 1
= 1/2