Existence of Limit Implies Continuity

This lecture discusses the relationship between the existence of a limit and continuity in functions. It covers the concept that a function's derivative is not arbitrary and cannot be the derivative of any function. The lecture also explores the implications of the function's graph being a derivative function, leading to the value at a specific point. Theorem 8.2 is presented, defining the conditions for a function to be continuous and differentiable within a given interval. The demonstration further illustrates the application of the theorem in determining the continuity and differentiability of functions.