Evaluate the limit: lim_{x -> 3} (x^2 - 9) / (x^2 - 2x - 3).
Answer and explanation
Correct answer: C. 3/2
- Step 1: Direct substitution yields 0/0. Step 2. Factor numerator: x^2 - 9 = (x - 3)(x + 3). Step 3. Factor denominator: x^2 - 2x - 3 = (x - 3)(x + 1). Step 4. Cancel (x - 3): lim (x + 3) / (x + 1). Step 5. Substitute x = 3: (3 + 3) / (3 + 1) = 6 / 4 = 3/2. Answer: 3/2. Why not the others: 2/3 inverts numerator and denominator; 1 assumes identical linear terms; 3 fails to evaluate denominator.
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