Calculus: a limitless perspective. 27: Error in the linear approximation

A novel approach to calculus using the intuitive idea of "best approximation" as the foundational tool, eliminating the need for limits. Video 27 uses the Cauchy Mean Value theorem to show the error in the "best linear approximation" is given by the second derivative times a simple quadratic. An explicit formula is given for the error term. Content by professors Michael Lamoureux and Matt Yedlin, with technical assistance from Andrew Wang at UBC Studios. Details on limitless calculus are published on the Arxiv at https://arxiv.org/abs/2510.20836