Approximation of Functions by Taylor Polynomials

This lecture covers the approximation of functions by Taylor polynomials, discussing the construction of polynomial approximations, the Taylor formula, the concept of Taylor series, and the conditions for a function to have a local minimum or maximum. The instructor explains the theory behind Taylor polynomials, demonstrates the uniqueness of Taylor expansions, and shows how to calculate limits using Taylor expansions. Examples are provided to illustrate the application of Taylor polynomials in solving mathematical problems.