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

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

Prepare for the DAY 2002A Limits Test with our targeted quiz. Test your understanding with flashcards and multiple-choice questions. Each question features hints and explanations to enhance your learning. Ace your exam!

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.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy