Limits of Functions in Several Variables

This lecture covers the concept of limits of functions in several real variables, including the characterization of limits using convergent sequences, the two gendarmes theorem, and the theorem stating that a continuous function on a compact set attains its minimum and maximum. Examples and demonstrations are provided to illustrate these concepts, such as determining the existence of limits using polar coordinate transformations and showcasing the maximum and minimum of a function on a compact set. The lecture also discusses the continuity of composite functions and provides insights into determining the existence of limits through sequential analysis.