Evaluate the limit as x approaches infinity of ln(1+x) / x.

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Multiple Choice

Evaluate the limit as x approaches infinity of ln(1+x) / x.

Explanation:
As x grows without bound, logarithmic growth is far slower than linear growth. The limit asks how fast ln(1+x) increases compared to x, and both numerator and denominator go to infinity, so L'Hôpital's rule applies. Differentiating gives the limit as lim_{x→∞} 1/(1+x), which clearly tends to 0. Thus the ratio ln(1+x) / x goes to 0.

As x grows without bound, logarithmic growth is far slower than linear growth. The limit asks how fast ln(1+x) increases compared to x, and both numerator and denominator go to infinity, so L'Hôpital's rule applies. Differentiating gives the limit as lim_{x→∞} 1/(1+x), which clearly tends to 0. Thus the ratio ln(1+x) / x goes to 0.

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