Continuity

Defined at point: $f (a)$ must exist (no holes or asymptotes).
Limit exists: $lim_{x \to a} f (x)$ must exist (Left-hand limit = Right-hand limit).
Consistency: The limit as $x$ approaches $a$ must exactly equal the function's value at $a$ , i.e., $lim_{x \to a} f (x) = f (a)$ . This ensures there is no 'jump' at $a$ .

This easy difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of continuity. It appeared in the 2025 exam.

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Continuity

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