Taylor Polynomials: Approximating Functions

This lecture introduces Taylor polynomials as a method to approximate functions around a point. The instructor explains the concept by deriving polynomials of different degrees for functions like exponential and sine, highlighting the importance of the remainder term in the approximation. Through examples with exponential and sine functions, the lecture demonstrates how higher-degree polynomials provide better approximations, emphasizing the significance of the Taylor series in representing functions accurately.