1. The problem asks to evaluate the limit $$\lim_{x \to 0} \frac{\sin(7x)}{x}$$. 2. We recognize a standard limit: $$\lim_{u \to 0} \frac{\sin u}{u} = 1$$. 3. To use this, substitute $$u = 7x$$, so as $$x \to 0, u \to 0$$. 4. Rewrite the limit as $$\lim_{x \to 0} \frac{\sin(7x)}{x} = \lim_{x \to 0} \frac{\sin u}{x}$$. 5. Express $$x$$ in terms of $$u$$: since $$u = 7x$$, then $$x = \frac{u}{7}$$. 6. Substitute back: $$\lim_{u \to 0} \frac{\sin u}{\frac{u}{7}} = \lim_{u \to 0} \frac{\sin u}{u} \cdot 7$$. 7. Using the standard limit: $$\lim_{u \to 0} \frac{\sin u}{u} = 1$$. 8. Therefore, the limit is $$1 \times 7 = 7$$. 9. However, since 7 is not among the options, there might be a typo in the options or problem. 10. If options must be chosen, none matches exactly. The technically correct answer is 7.