To find the limit of \(\lim_{x \to 0} \ln(1 + x)\), we can use the fact that \(\ln(1 + x)\) is continuous and differentiable around \(x = 0\). Here's a step-by-step solution:

1. **Recognize the behavior of \(\ln(1 + x)\) around \(x = 0\):**
   The natural logarithm function \(\ln(1 + x)\) is defined for \(x > -1\). Near \(x = 0\), we can use the fact that the logarithm function is continuous.

2. **Apply the limit:**
   \[
   \lim_{x \to 0} \ln(1 + x)
   \]
   As \(x\) approaches 0, \(1 + x\) approaches 1.

3. **Evaluate the natural logarithm at 1:**
   \[
   \ln(1) = 0
   \]

Thus, the limit is:
\[
\lim_{x \to 0} \ln(1 + x) = 0
\]

Would you like more details or have any questions about this solution? Here are some questions you might consider next:

1. What is the derivative of \(\ln(1 + x)\)?
2. How can we apply L'Hôpital's Rule to find limits involving logarithms?
3. What are some common logarithmic limits to know?
4. How does the Taylor series expansion of \(\ln(1 + x)\) help in evaluating limits?
5. Can we find limits of logarithmic functions approaching infinity?

**Tip:** When evaluating limits involving logarithmic functions, consider using properties of logarithms and continuity to simplify the problem.

Learn how to evaluate the limit \(\lim_{x \to 0} \ln(1 + x)\) step-by-step. Understand the behavior of the natural logarithm function near 0 and apply the limit definition to find the result, which is 0. Suitable for advanced high school students and anyone interested in calculus limits involving logarithmic functions.

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