Should assume that it is an Nth degree polynomial centered at a. We have to keep writing it over and over but you Something like N comma a to say it's an Nth degreeĪpproximation centered at a. And sometimes you might seeĪ subscript, a big N there to say it's an Nth degree approximation and sometimes you'll So our polynomial, our Taylor polynomial approximation would look

And that polynomial evaluated at a should also be equal to thatįunction evaluated at a.

Polynomial evaluated at a should be equal to the derivatives of our function evaluated at a. Of the polynomial, those derivatives of that The Taylor polynomialĬomes out of the idea that for all of the derivatives up to and including the degree So I want a Taylor polynomialĬentered around there. So this is the x-axis, this is the y-axis. Wanna approximate f of x with a Taylor polynomial centered around x is equal to a. So, that's my y-axis, that is my x-axis and maybe f of x looks That we have some function f of x right over here.

Lagrange error bound