Step-by-Step Solution
Key Concept: $\frac{x}{2^x - 1} \cdot 2^x$. As $x \to 0$: $2^x \to 1$ and $\frac{x}{2^x - 1} \to \frac{1}{\ln 2}$ (standard limit: $\lim_{x \to 0} \frac{a^x - 1}{x} = \ln a$). Product $\to \frac{1}{\ln 2}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)