Lagrange Remainder

analysis

Definition

Lagrange Remainder

Let be -times differentiable on an interval containing and . The Lagrange remainder is the error term in the Taylor expansion of of order .

There exists a point between and such that:

This form of the remainder is useful for bounding the error of a Taylor polynomial approximation.

Error Bounding

If the -th derivative is bounded on the interval, i.e., for all between and , then the error is bounded by: