Taylor's Theorem: Lagrange Form for Approximating Error

[marshmellow]

If the integral form of the remainder term gives the exact error, why do we use the Lagrange form of the remainder to approximate the error.

 

[lurflurf]

All the common forms of the remainder Cauchy, Lagrange and Schlömilch; are not helpful in exact form. The exact answer is hard to compute. A simple approximation often is more useful than a complicated exact value.

 

[marshmellow]

Oh! that's so simple, thanks.