To find the limit of \(\ln(1 + x)\) as \(x\) approaches 0, we can use the definition of the natural logarithm function and its properties. 

\[
\lim_{x \to 0} \ln(1 + x)
\]

As \(x\) approaches 0, \(1 + x\) approaches 1. The natural logarithm function, \(\ln(y)\), is continuous at \(y = 1\). Therefore, we can directly substitute \(1\) into the natural logarithm:

\[
\lim_{x \to 0} \ln(1 + x) = \ln(1) = 0
\]

So,

\[
\lim_{x \to 0} \ln(1 + x) = 0
\]

Do you want details or have any questions? Here are five questions you can ask:

1. How do I solve limits involving trigonometric functions?
2. Can you explain L'Hôpital's rule with an example?
3. What is the limit of \(\frac{\sin(x)}{x}\) as \(x\) approaches 0?
4. How do I find the derivative of a logarithmic function?
5. Can you explain the concept of continuity in calculus?

Tip: Understanding the properties of logarithmic and exponential functions can greatly simplify solving limits and derivatives involving these functions.

Learn how to find the limit of ln(1 + x) as x approaches 0 using the definition of the natural logarithm and its properties. Understand the continuity of the natural logarithm function at y = 1. Suitable for undergraduate students studying calculus and limits.

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