Question Detail

MTH 102 Limits Objective Question

Question

Evaluate the limit of \( \frac{\ln(1 + x^{-1})}{x^{-1}} \) as \( x \) tends to infinity.
Options
A 0
B 1
Correct Answer
C e
D Infinity
Correct Answer

Option B is the correct answer.

Detailed Explanation

Let ( u = x^{-1} ). As ( x \to \infty ), ( u \to 0 ). The limit ( \lim_{u \to 0} \frac{\ln(1+u)}{u} = 1 ).

Hint

Model Question 17.

Question Info