$\lim_{x \to \infty} x[\ln(x + a) - \ln x] = \dots$ (Express your answer in terms of $a$.)
Step-by-Step Solution
Key Concept: $x \ln\frac{x + a}{x} = x \ln\left(1 + \frac{a}{x}\right) \approx x \cdot \frac{a}{x} = a$ as $x \to \infty$ (since $\ln(1 + u) \approx u$ for $u \to 0$).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: a