Taylor's approximation: Mean Value Theorem, l'Hopital rule, Examples

This lecture covers the application of the Mean Value Theorem, the l'Hopital rule, and Taylor's approximation formula with examples. It also discusses the derivative and monotone functions, along with the concept of strictly increasing and decreasing functions. The lecture explores the development of functions to the nth order around a point, the uniqueness of Taylor's formula, and the control of error in an approximation. It concludes with the expansion and composition of functions, showcasing the computation of the expansion of a composite function using Taylor's formula.