Limits in Function Analysis

This lecture covers the fundamental concept of limits in function analysis, starting with the definition of limits for functions defined in the neighborhood of a point. The instructor explains how to determine the limit of a function as it approaches a specific point, using the theory developed for sequences. Various examples are provided to illustrate the calculation of limits for different types of functions, including polynomials and rational functions. The lecture also explores the properties of limits under algebraic operations and the uniqueness of limits. Additionally, the instructor demonstrates the application of the squeeze theorem to evaluate limits in complex scenarios, emphasizing the importance of understanding and applying limit properties in mathematical analysis.