Taylor Polynomials: Correction Term

This lecture delves into the concept of the correction term in Taylor polynomials. Starting with the convergence of Taylor polynomials for the natural logarithm, the instructor explores how increasing the degree of the polynomial around a point improves the approximation. The lecture then introduces the correction term, which quantifies the error between the function and its Taylor polynomial. Through theorems and demonstrations, the instructor illustrates how to calculate and interpret the correction term. Examples with cosine and exponential functions showcase the refinement of approximations with higher polynomial degrees, hinting at the convergence to the exact function value.