### Pages similar to: Historical and theoretical comments: Mean Value Theorem

- Taylor polynomials: formulas

Different ways of writing Taylor's formula with remainder term. - Determining tolerance/error in Taylor polynomials.

Calculating with what tolerance a Taylor polynomial approximates a function on an interval. - How large an interval with given tolerance for a Taylor polynomial?

Given a Taylor polynomial expanded around a point, on how large an interval around the point does it achieve a required tolerance? - Achieving desired tolerance of a Taylor polynomial on desired interval

For a given interval around a point, how many terms of a Taylor polynomial expanded around that point must be used to achieve a required tolerance? - Classic examples of Taylor polynomials

Some of the most famous (and important) examples of Taylor expansions. - Computational tricks regarding Taylor polynomials

A short cut to calculating Taylor polynomials in terms of Taylor polynomials of simple functions. - Integrating Taylor polynomials: first example

An example showing how to integrate a Taylor polynomial and interpret the result. - Prototypes: More serious questions about Taylor polynomials

Questions regarding using Taylor polynomials to approximate a function over an interval. - Integrating the error term of a Taylor polynomial: example

An example showing how to integrate the error term of Taylor polynomial and interpret the result. - Linear approximations: approximation by differentials

Approximating the value of a function near a point by its tangent line formula. - Trigonometric integrals

Using trigonometric identities to calculate integrals involving trigonometric functions. - Intermediate Value Theorem, location of roots

Using the Intermediate Value Theorem to find small intervals where a function must have a root. - A refresher on the chain rule

How to compute the derivative of a composition of functions. - Exponential growth and decay: a differential equation

Solving a differential equation to find an unknown exponential function. - Implicit differentiation

Differenting a function that is defined implicitly in terms of a relation between two variables. - Approximating functions by quadratic polynomials

Determining how to use information from the second derivative to form a quadratic approximation to a function. - Area and definite integrals

Integrating to find the area under a curve or the area between two curves. - Minimization and maximization refresher

How to calculate the maxima and minima of a differentiable function. - An algebra trick for finding critical points

An old algebraic trick that can make finding critical points much easier. - Related rates

Calculating one derivative in terms of another derivative.