Question

state taylor's theorem of differential calculus?

Answer 1

In calculus, Taylor's theorem gives an approximation of a k-times differentiablefunction around a given point by a k-th orderTaylor polynomial. For analytic functions the Taylor polynomials at a given point are finite-order truncations of its Taylor series, which completely determines the function in some neighborhood of the point. The exact content of "Taylor's theorem" is not universally agreed upon. Indeed, there are several versions of it applicable in different situations, and some of them contain explicit estimates on the approximation error of the function by its Taylor polynomial.