Denoted as limx to a fx - Study guides, Class notes & Summaries

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 Concepts:1.Continuity:oA 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...