Solution: Using L'Hôpital's Rule, we differentiate the numerator and denominator to find lim (x -> 0) (1/(1 + x)) = 1.
Steps: 9
Step 1: Identify the limit we want to calculate: lim (x -> 0) (ln(1 + x)/x).
Step 2: Notice that if we plug in x = 0 directly, we get ln(1 + 0)/0, which is 0/0. This is an indeterminate form.
Step 3: Since we have an indeterminate form, we can use L'Hôpital's Rule. This rule states that we 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: Now we can rewrite the limit using the derivatives: lim (x -> 0) (1/(1 + x)/1).
