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This lecture covers the definitions and theorems related to function limits, including the concept of right and left limits, algebraic operations on limits, and the theorem of the two gendarmes for functions. It also explores examples illustrating the application of these concepts. The instructor explains how to determine limits using sequences and demonstrates the algebraic laws governing limits. Additionally, the lecture delves into infinite limits and their behavior, emphasizing the importance of understanding the behavior of functions as they approach certain values.