Lagrange Form of the Remainder Term in a Taylor Series

The Lagrange form of the remainder term in a Taylor series is a crucial concept in calculus and mathematical analysis. Named after Joseph-Louis Lagrange, this theorem provides an estimation of the error between a function and its Taylor polynomial approximation. It plays a fundamental role in approximating functions and understanding their behavior locally around a point. By quantifying the error, it enables mathematicians and scientists to assess the accuracy of polynomial approximations, making it an indispensable tool in various fields such as physics, engineering, and economics.