Pages similar to: Determining tolerance/error in Taylor polynomials.
- Taylor polynomials: formulas
Different ways of writing Taylor's formula with remainder term. - 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. - Prototypes: More serious questions about Taylor polynomials
Questions regarding using Taylor polynomials to approximate a function over 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? - Integrating Taylor polynomials: first example
An example showing how to integrate a Taylor polynomial and interpret the result. - 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. - The idea of the derivative of a function
The derivative of a function as the slope of the tangent line. - Derivatives of polynomials
How to compute the derivative of a polynomial. - Derivatives of more general power functions
How to compute the derivative of power functions. - A refresher on the quotient rule
How to compute the derivative of a quotient. - A refresher on the product rule
How to compute the derivative of a product. - A refresher on the chain rule
How to compute the derivative of a composition of functions. - Related rates
Calculating one derivative in terms of another derivative. - Intermediate Value Theorem, location of roots
Using the Intermediate Value Theorem to find small intervals where a function must have a root. - Derivatives of transcendental functions
A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. - L'Hospital's rule
A way to simplify evaluation of limits when the limit is an indeterminate form. - The second and higher derivatives
Taking derivatives multiple times to calculate the second or higer derivative. - Inflection points, concavity upward and downward
Finding points where the second derivative changes sign.