Find lim x→1 (1 - x^2) / ln(x).
Choose 1 answer:
A) -2
B) -1
C) 0
D) The limit doesn't exist.

Question

Find lim x→1 (1 - x^2) / ln(x). Choose 1 answer: A) -2 B) -1 C) 0 D) The limit doesn't exist.

SnapAndSolve AI · Accepted Answer

To solve this limit, we can use L'Hôpital's Rule because both the numerator and the denominator approach 0 as x approaches 1. L'Hôpital's Rule states that if the limit of f(x)/g(x) as x approaches a point results in an indeterminate form 0/0, then the limit is the same as the limit of their derivatives, provided this limit exists.

Differentiate the numerator: d/dx (1 - x^2) = -2x.
Differentiate the denominator: d/dx (ln(x)) = 1/x.
Apply L'Hôpital's Rule: lim x→1 (-2x) / (1/x) = lim x→1 (-2x^2).
Evaluate the limit: -2(1)^2 = -2.

Answer: A) -2

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Find lim x→1 (1 - x^2) / ln(x). Choose 1 answer: A) -2 B) -1 C) 0 D) The limit doesn't exist.

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