Compute lim_{x->2} (x^2 - 4)/(x - 2).

Compute lim_{x->2} (x^2 - 4)/(x - 2).

• A. 0
• B. 4
• C. -4
• D. 2

Answer: (B)

When a limit hits a point where the substitution would give 0/0, look to factor and simplify. The numerator x^2 - 4 factors as (x - 2)(x + 2). Cancelling the common factor with the denominator leaves the expression x + 2 for x ≠ 2. So as x approaches 2, the expression behaves like x + 2, which tends to 4. The original expression is not defined at x = 2, but the limit exists and equals 4. This rules out 0, 2, and -4 as the limit; the correct limit is 4.

When a limit hits a point where the substitution would give 0/0, look to factor and simplify. The numerator x^2 - 4 factors as (x - 2)(x + 2). Cancelling the common factor with the denominator leaves the expression x + 2 for x ≠ 2. So as x approaches 2, the expression behaves like x + 2, which tends to 4. The original expression is not defined at x = 2, but the limit exists and equals 4. This rules out 0, 2, and -4 as the limit; the correct limit is 4.