topic 21Questiontopic 2.4connecting differentiability and continuityAnswer & ExplanationDifferentiability and continuity are two fundamental concepts in calculus that are closely related, yet distinct. Understanding their connection is crucial for analyzing the behavior of functions.Key Conce...
topic 2.4connecting differentiability and continuity
Answer & Explanation
Differentiability and continuity are two fundamental concepts in calculus that
are closely related, yet distinct. Understanding their connection is crucial for
analyzing the behavior of functions.
Key Concepts:
1. Continuity:
o A function ( f(x) ) is continuous at a point ( x = a ) if:
1. ( f(a) ) is defined.
2. The limit of ( f(x) ) as ( x \to a ), denoted as ( \lim_{x \to a}
f(x) ), exists.
3. The limit equals the function value: ( \lim_{x \to a} f(x) =
f(a) ).
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