Lim = cos 3x - cos x / x. Sin 2x x-> 0

Lim = cos 3x – cos x / x. Sin 2x
x-> 0

Jawaban Terkonfirmasi

$ingat: boxed{cos a-cos b=-2sin frac{1}{2}(a+b).sin frac{1}{2}(a-b) } \ \ cos 3x-cos x=-2sin frac{1}{2}(3x+x).sin frac{1}{2}(3x-x) \ ~~~~~~~~~~~~~~~~~~=-2sin frac{1}{2}(4x).sin frac{1}{2}(2x) \ ~~~~~~~~~~~~~~~~~~=-2sin 2x.sin x \ \ displaystyle lim_{x to0} frac{cos 3x-cos x}{x.sin 2x} \ = lim_{x to0} frac{-2sin 2x.sin x}{x.sin 2x} \ =lim_{x to0} frac{-2sin 2x}{sin 2x} . frac{sin x}{x} \ =-2.1.1 \ =-2$

semoga membantu ya 🙂