Real Functions: Limit at a Point

This lecture delves into real functions, focusing on the limit at a point. The instructor introduces the concept by drawing two functions, one with a hole at x=2. By comparing the behavior of the functions as x approaches 2, the idea of limit is explored. The notion of neighborhood around a point is introduced, leading to the definition of limit. The instructor illustrates the concept with graphical examples and analytical approaches, emphasizing the importance of understanding limits in calculus. The lecture concludes with discussions on left and right limits, showcasing how to determine limits in complex functions through examples and theorems.