Free trial lesson

U10.11 Taylor Polynomials and Lagrange Error Bound

Build Taylor polynomial approximations T_n(x) of f about x = c using f(c), f'(c), ..., f^(n)(c). Apply Lagrange error bound: |R_n(x)| ≤ M·|x − c|^{n+1}/(n+1)! where M bounds |f^{(n+1)}|.