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).

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).