If f(x) = (x² − 4)/(x − 2) for x ≠ 2, and f(x) = k for x = 2 is continuous at x = 2, then the value of k is:

If f(x) = (x² − 4)/(x − 2) for x ≠ 2, and f(x) = k for x = 2 is continuous at x = 2, then the value of k is:

• A. 2
• B. 4
• C. 0
• D. Not defined

Answer: B) 4

Explanation: For continuity at x = 2, lim(x→2) f(x) = f(2). lim(x→2) (x² − 4)/(x − 2) = lim(x→2) (x − 2)(x + 2)/(x − 2) = lim(x→2) (x + 2) = 4. Hence, k = 4.