Calculus II, Lecture 19: Polynomial approximation

Lecture 19: Polynomial approximations.

A classic problem from differential calculus asks for a "tangent line approximation" to a function at a point. This is simply an approximation of a function by a degree-1 polynomial, sometimes called "first order". One could similarly ask for a "quadratic approximation", which would be an approximation by a degree-2 polynomial, sometimes called "2nd order." Naturally, one could ask for an n'th order approximation for any n, and this is called a "Taylor polynomial of order n."