Nomor 14
Selesaikan limit trigonomettri berikut
\( \begin{aligned} \displaystyle \lim\limits_{x \to 0} \left (\frac{\sin x - \tan x} {x^2 \tan x} \right) &= \lim\limits_{x \to 0} \left (\frac{\sin x - \frac{\sin x}{\cos x}} {x^2 \frac{\sin x}{\cos x}} \times \frac{\sin x \cos x}{\sin x \cos x} \right)\\ &= \lim\limits_{x \to 0} \left (\frac{\sin^2 x \cos x - \sin^2 x} {x^2 \sin^2 x} \right)\\ &= \lim\limits_{x \to 0} \left (\frac{\sin^2 x (\cos x - 1)} {x^2 \sin^2 x} \right)\\ &= \lim\limits_{x \to 0} \left (\frac{\sin^2 x} {x^2} \right) \times \lim\limits_{x \to 0} \left (\frac{\cos x - 1} {\sin^2 x} \right)\\ &= \lim\limits_{x \to 0} \left (\frac{\sin x} {x} \right)^2 \times \lim\limits_{x \to 0} \left (\frac{\cos x - 1} {1 - \cos^2 x} \right)\\ &= \left (\frac{1}{1} \right)^2 \times \lim\limits_{x \to 0} \left (\frac{\cos x - 1} {1 - \cos^2 x} \right)\\ \end{aligned} \)