Taylor Polynomials: Approximating Functions with Taylor Polynomials

This lecture explores the concept of Taylor polynomials, focusing on how increasing the order of the Taylor polynomial improves the approximation of function values for a given x. It discusses examples with cos(x), exp(x), and ln(x), showing how the correction term tends to zero as the order of the polynomial increases. The lecture also demonstrates how Taylor polynomials can be used to calculate limits of functions, even when the function is not well-defined at a certain point.