This lecture covers the development of limited order 1 and 2, focusing on linearity and polynomial approximation. It explains the concepts of Taylor polynomials of order 1 and 2, linear approximation, and polynomial degree. The instructor discusses the development of limited order 1 and 2, emphasizing the linearity and approximation of functions around a point. The lecture also delves into the Taylor polynomials of order 1 and 2, showcasing their applications in function approximation.