If f(x) = (x² − 1)/(x − 1) for x ≠ 1 and f(1) = 2, then at x = 1, f is: A. continuous B. discontinuous with removable discontinuity C. discontinuous with jump discontinuity D. infinite discontinuity Answer: A) continuous Explanation: lim(x→1) (x²−1)/(x−1) = lim(x→1) (x+1) = 2 = f(1). So continuous.

imo class 12 continuity and differentiability

If f(x) = (x² − 1)/(x − 1) for x ≠ 1 and f(1) = 2, then at x = 1, f is:

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If f(x) = (x² − 1)/(x − 1) for x ≠ 1 and f(1) = 2, then at x = 1, f is:

Answer: A) continuous

Explanation: lim(x→1) (x²−1)/(x−1) = lim(x→1) (x+1) = 2 = f(1). So continuous.