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Explore the fundamental concept of continuity in functions through this comprehensive lecture. Delve into the intricacies of continuous functions, their properties, and their significance in calculus. Learn to identify and analyze discontinuities, understand the importance of limits in determining continuity, and grasp the practical applications of this crucial mathematical concept. Gain valuable insights from Professor Leonard's clear explanations and illustrative examples, enhancing your understanding of this essential topic in Calculus 1.