Lim 1 - cos x ____________ cos 3x - cos x X->0

Lim 1 – cos x
____________
cos 3x – cos x
X–>0

Jawaban Terkonfirmasi

Mengenal:
$boxed{cos A-cos B=-2sin(frac{A+B}{2})sin(frac{A-B}{2})}$
Maka,
$$begin{align}lim_{xto0}frac{1-cos x}{cos 3x-cos x}&=lim_{xto0}frac{2sin^2frac{1}{2}x}{-2sin(frac{3x+x}{2})sin(frac{3x-x}{2})} \ &=lim_{xto0}frac{-sin^2frac{1}{2}x}{sin 2xsin x} \ &=-lim_{xto0}frac{sinfrac{1}{2}x}{sin 2x}timeslim_{xto0}frac{sinfrac{1}{2}x}{sin x} \ &=-frac{^1/_2}{2}timesfrac{^1/_2}{1} \ &=-frac{1}{4}timesfrac{1}{2} \ &=-frac{1}{8}end{align}$

Lim    2sin^2 1/2 x
X->0 -2sin 2x.sin x
Lim   2sin 1/2 x . sin 1/2 x
X->0   -2sin 2x.sin x
2 . 1/2 . 1/2
-2 . 2 . 1
1/2 = -1/8
-4