Interesting Way to Derive Taylor Series(Error Minimization)

We derive the Taylor Series by starting with a linear approximation and finding such coefficients to make the normalised error go to zero, which gives us the best possible approximation. Then we extend the polynomial to degree 2 and do the same thing again, each time finding the coefficients that make that nth degree polynomial the best possible approximation to our function at a point(as no other combination of coefficients would make the normalised error go to zero). This will give us exactly the Taylor Series of our function, and we can therefore see that the Taylor Expansion is the best possible approximation of a function we can find.

Видео Interesting Way to Derive Taylor Series(Error Minimization) канала Physics and Math