lightbulb
Key Concepts
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1. Continuity at a Point
A function f(x) is continuous at x = a if:
- f(a) is defined.
- lim (x→a) f(x) exists.
- lim (x→a) f(x) = f(a).
Conditions: LHL = RHL = f(a).
2. Differentiability
Every differentiable function is continuous, but the converse is not necessarily true (e.g., |x| is continuous but not differentiable at x=0).