Step 1: Identify the limit we want to evaluate: lim (x -> 0) (ln(1 + x)/x).
Step 2: Check if the limit is in an indeterminate form. As x approaches 0, ln(1 + x) approaches ln(1) which is 0, and x approaches 0. So we have 0/0, which is indeterminate.
Step 3: Apply L'Hôpital's Rule, which states that if you have an indeterminate form like 0/0, you can take the derivative of the numerator and the derivative of the denominator.
Step 4: Differentiate the numerator: The derivative of ln(1 + x) is 1/(1 + x).
Step 5: Differentiate the denominator: The derivative of x is 1.
Step 6: Rewrite the limit using the derivatives: lim (x -> 0) (1/(1 + x))/1.
