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f(x) is discontinuous at x = a if which condition fails?
AAny of the above failing makes f discontinuous
Bf(a) defined
CLimit at x = a exists
Df(a) equals the limit at x = a
Answer & Solution
Correct answer: A. Any of the above failing makes f discontinuous
Continuity requires all 3 conditions. Failure of any one creates discontinuity. Different types: removable (limit exists but f(a) wrong), jump (one-sided limits differ), infinite (limit is ±∞), oscillating (no limit).
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