Evaluate the Limit

Problem

(lim_x→0)(ln(x))

Solution

1. Identify the domain of the natural logarithm function ƒ(x)=ln(x) which is (0,∞)

2. Determine the direction of the limit, as x can only approach 0 from the right side (x→0 for the function to be defined.

3. Analyze the behavior of the natural logarithm as the input x becomes an arbitrarily small positive number.

4. Observe that as x gets closer to 0 the value of ln(x) decreases without bound toward negative infinity.

Final Answer

(lim_x→0)(ln(x))=−∞

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