প্রশ্ন: \( \lim_{x \to 0} \frac{\sin 7x - \sin x}{\sin 6x} = ? \)

সমাধান:

আমরা জানি, \( \lim_{x \to 0} \frac{\sin x}{x} = 1 \)

তাহলে,

\( \lim_{x \to 0} \frac{\sin 7x - \sin x}{\sin 6x} \) \( = \lim_{x \to 0} \frac{\frac{\sin 7x}{x} - \frac{\sin x}{x}}{\frac{\sin 6x}{x}} \) \( = \lim_{x \to 0} \frac{\frac{\sin 7x}{7x} \cdot 7 - \frac{\sin x}{x}}{\frac{\sin 6x}{6x} \cdot 6} \) \( = \frac{1 \cdot 7 - 1}{1 \cdot 6} \) \( = \frac{6}{6} \) \( = 1 \)

সুতরাং, উত্তর: 1