Taylor Series: Approximating Functions with Polynomials

This lecture focuses on using Taylor series to approximate functions with polynomials, starting with the concept of development limité. The instructor explains how to approximate functions like the sine and cosine using polynomials of increasing degrees, highlighting the precision achieved as the degree increases. The lecture delves into the convergence and divergence of series, exploring the conditions under which a function can be represented by a series. Various examples, including the exponential and logarithmic functions, demonstrate the application of Taylor series in approximating functions. The lecture concludes with a discussion on the limitations of series in representing certain functions.