Calculus

Using standard trigonometric limits: $\lim_{x \to 0} \frac{\sin(4x)}{\tan(2x)} = \lim_{x \to 0} \frac{\frac{\sin(4x)}{4x} \cdot 4x}{\frac{\tan(2x)}{2x} \cdot 2x} = \frac{1 \cdot 4}{1 \cdot 2} = 2.0$