Evaluate the limit as x approaches 3 of (x^2 - 9)/(x - 3).

Evaluate the limit as x approaches 3 of (x^2 - 9)/(x - 3).

• A. 6
• B. 0
• C. -6
• D. 3

Answer: (A)

The limit hinges on removing a removable discontinuity by factoring. The numerator x^2 − 9 factors as (x − 3)(x + 3). This allows the (x − 3) factor to cancel with the denominator, leaving the simpler expression x + 3 for all x ≠ 3. Because the only issue at x = 3 is the hole created by the original 0/0 form, the limit matches the value of the simplified expression as x approaches 3. Evaluate the simplified expression at x = 3: 3 + 3 = 6. Therefore, the limit is 6. Direct substitution into the original form gives 0/0, which is undefined, so canceling the common factor reveals the actual limit.

The limit hinges on removing a removable discontinuity by factoring. The numerator x^2 − 9 factors as (x − 3)(x + 3). This allows the (x − 3) factor to cancel with the denominator, leaving the simpler expression x + 3 for all x ≠ 3. Because the only issue at x = 3 is the hole created by the original 0/0 form, the limit matches the value of the simplified expression as x approaches 3. Evaluate the simplified expression at x = 3: 3 + 3 = 6. Therefore, the limit is 6. Direct substitution into the original form gives 0/0, which is undefined, so canceling the common factor reveals the actual limit.