Evaluate lim_{x→1} (x^2 - 1)/(x - 1).

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Multiple Choice

Evaluate lim_{x→1} (x^2 - 1)/(x - 1).

Explanation:
Cancellation of a common factor lets you resolve an indeterminate form. The numerator x^2 - 1 factors as (x - 1)(x + 1), so the expression becomes [(x - 1)(x + 1)]/(x - 1). For x ≠ 1 you can cancel (x - 1), leaving x + 1. Take the limit as x approaches 1 to get 1 + 1 = 2. Direct substitution would give 0/0, which isn’t informative, but the simplification shows the limit clearly.

Cancellation of a common factor lets you resolve an indeterminate form. The numerator x^2 - 1 factors as (x - 1)(x + 1), so the expression becomes [(x - 1)(x + 1)]/(x - 1). For x ≠ 1 you can cancel (x - 1), leaving x + 1. Take the limit as x approaches 1 to get 1 + 1 = 2. Direct substitution would give 0/0, which isn’t informative, but the simplification shows the limit clearly.

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