1. **State the problem:** Evaluate the limit $$\lim_{x \to 0} \frac{\sin 3x}{x}$$. 2. **Recall the standard limit:** We know that $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$. 3. **Rewrite the expression:** To use the standard limit, rewrite the expression as $$\frac{\sin 3x}{x} = \frac{\sin 3x}{3x} \cdot 3$$. 4. **Apply the limit:** As $$x \to 0$$, $$\lim_{x \to 0} \frac{\sin 3x}{3x} = 1$$ by the standard limit. 5. **Calculate the final limit:** $$\lim_{x \to 0} \frac{\sin 3x}{x} = 3 \cdot 1 = 3$$. **Final answer:** $$3$$.