Evaluate natural log of infinity

Problem

(lim_x→∞)(ln(x))

Solution

1. Identify the behavior of the natural logarithm function ƒ(x)=ln(x) as the input x increases without bound.

2. Observe that the natural logarithm is an increasing function for all x>0 meaning as x gets larger, ln(x) also gets larger.

3. Determine the limit by noting that there is no horizontal asymptote; the function grows to infinity, albeit slowly.

Final Answer

(lim_x→∞)(ln(x))=∞

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