Mathematics : Approximation of Functions

Taylor's formula

Let f be a function that has derivatives up to the n-th order on an interval about x₀ = 0. Using the Taylor's formula we can approximate f(x) near x₀=0 by a polynomial.

____ APPROXIMATIONS OF FUNCTION BY POLINOMIALS

____ ⁽¹⁾  TAYLOR'S POLINOMIAL

____ ⁽²⁾  ERROR OR REMAINDER (LAGRANGE)

: IMAGE/APPLET : Taylor's formula :
  (if applet running) Points you can move → x₀, c, I_(x0)