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Find lim (xe^x - e) / (x^2 - 1) as x approaches 1. Choose 1 answer: A) e/2 B) e C) 1/2 D) The limit doesn't...

Find lim (xe^x - e) / (x^2 - 1) as x approaches 1.
Choose 1 answer:
A) e/2
B) e
C) 1/2
D) The limit doesn't exist.

Answer

To find the limit, we can apply L'Hôpital's Rule since the limit results in an indeterminate form 0/0 when x = 1.

Differentiate the numerator: d/dx (xe^x - e) = e^x(x + 1).
Differentiate the denominator: d/dx (x^2 - 1) = 2x.
Apply L'Hôpital's Rule: lim (x→1) (e^x(x + 1)) / (2x).
Substitute x = 1: (e(1 + 1)) / (2 * 1) = 2e / 2 = e.

The correct answer is B) e.

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