Question Detail

MTH 102 Limits Objective Question

Question

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

Option B is the correct answer.

Detailed Explanation

As ( x \to \infty ), ( \frac{1}{x} \to 0 ). The expression becomes ( \frac{e^0 - e^0}{e^0 + e^0} = \frac{0}{2} = 0 ).

Hint

Exercise 1.1, Question 29.

Question Info