Mixed: Lagrange's and Cauchy's Remainders Form

Sometimes numerical methods are needed to solve mathematical problems, especially in applied problems. The numerical methods usually associated with errors, so the numerical solution is usually not equivalent to the exact solution, but if the error could be estimated then the exact solution could be known. The Lagrange's and Cauchy's remainders are two poplar methods to calculate the remainder and the generalization of them is known Schloemilch-Roeche?s remainder. By comparing: the Lagrange's and Cauchy's remainders methods for some functions at a point x, it could be seen that the Lagrange method has more accuracy if c is in a neighborhood of x_0, while the Cauchy method gives better results if cis somewhere near the middle between x_0andx.