alleryA function f is continuous at x = a if and only if:
Alim_{x→a} f(x) exists AND equals f(a)
Bf(a) is finite (continuity just means defined)
Cf is differentiable at a (this is stronger)
Dlim_{x→a-} f(x) exists (only LHL needed)
Answer & Solution
Correct answer: A. lim_{x→a} f(x) exists AND equals f(a)
**Continuity at a requires:**
(1) f(a) defined; (2) lim_{x→a} f(x) exists (LHL = RHL)
(3) lim equals f(a). All three must hold.
Differentiability implies continuity, but not vice versa.
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