Question Detail

MTH 102 Limits Objective Question

Question

Evaluate the limit of \( \frac{e^{x-1} - x}{(x - 1)^2} \) as \( x \) tends to 1.
Options
A 1
B \(\frac{1}{2}\)
Correct Answer
C 0
D Infinity
Correct Answer

Option B is the correct answer.

Detailed Explanation

Applying L'Hospital's Rule twice results in ( \frac{e^{x-1}}{2} ). At ( x=1 ), this is ( \frac{1}{2} ).

Hint

Model Question 15.

Question Info