Lagrange Error Bound

Applying the Lagrange error bound to find a maximum interval for the error of a Taylor polynomial approximation.

Mapped to AP College Board # LIM-8, LIM-8.C, LIM-8.C.1, LIM-8.C.2

Power series allow us to represent associated functions on an appropriate interval. Determine the error bound associated with a Taylor polynomial approximation. The Lagrange error bound can be used to determine a maximum interval for the error of a Taylor polynomial approximation to a function. In some situations, the alternating series error bound can be used to bound the error of a Taylor polynomial approximation to the value of a function.