If (x^2-4)/(x-2) is simplified to x+2 for x ≠ 2, what is lim x->2 of the simplified expression?

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Multiple Choice

If (x^2-4)/(x-2) is simplified to x+2 for x ≠ 2, what is lim x->2 of the simplified expression?

Explanation:
The limit is determined by the value the expression approaches as x gets very close to 2. Here, the numerator factors as (x−2)(x+2), so the (x−2) cancels with the denominator for all x ≠ 2, leaving the simpler expression x+2. Near x = 2, the behavior is governed by this linear form, so the limit is obtained by plugging in x = 2: 2 + 2 = 4. The original expression isn’t defined at x = 2 due to division by zero, but the limit as x approaches 2 exists and equals 4.

The limit is determined by the value the expression approaches as x gets very close to 2. Here, the numerator factors as (x−2)(x+2), so the (x−2) cancels with the denominator for all x ≠ 2, leaving the simpler expression x+2. Near x = 2, the behavior is governed by this linear form, so the limit is obtained by plugging in x = 2: 2 + 2 = 4. The original expression isn’t defined at x = 2 due to division by zero, but the limit as x approaches 2 exists and equals 4.

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