Using Taylor's formula with a=0 and n=3, how would you find the cubic approximation of f(x)= 1/(1-x) at x=0, given the upper bound for the magnitude of the error in the approximation when lxl< 0.1 ?
Using Taylor's formula with a=0 and n=3, how would you find the cubic approximation of f(x)= 1/(1-x) at x=0, given the upper bound for the magnitude of the error in the approximation when lxl< 0.1 ?
The derivatives are
The Taylor polynomial and the Taylor remainder where c is between 0 and . Since then we are trying to determine the maximum of on the domain and so this would occur at and the maximum error would be