Gives the Lagrange form of the Taylor remainder, providing an explicit bound on the error of a Taylor polynomial approximation.

Defines the Maclaurin series as the special case of a Taylor series centered at zero, and lists key standard Maclaurin series.

Illustrates using the Maclaurin series of a function to evaluate indeterminate limits by series substitution.

Illustrates approximating non-elementary definite integrals by substituting a Maclaurin series for the integrand and integrating term by term.

Defines the Taylor series of an infinitely differentiable function about a point, using its higher-order derivatives.

Defines the n-th degree Taylor polynomial of a function centered at c, and the remainder term measuring its approximation error.