Question

Помогите пожалуйста номер 237

Answer 1

$\lim_{x \to 0} \frac{\sin^{2} 2x}{x^{2}}= \lim_{x \to 0} \frac{\frac{d}{d x} \sin^{2} 3x}{\frac{d}{d x} x^{2}} = \lim_{x \to 0} \frac{2\sin 4x}{2x} = \lim_{x \to 0} \frac{\sin 4x}{x} = \lim_{x \to 0} \frac{\frac{d}{d x} \sin 4x}{\frac{d}{d x} x} = \lim_{x \to 0} \frac{4\cos 4x}{1} = \lim_{x \to 0} 4\cos 4x = 4\cos (4\times 0) = 4$