Pages similar to: Approximating functions by quadratic polynomials
- Introduction to Taylor's theorem for multivariable functions
Development of Taylor's polynomial for functions of many variables. - Multivariable Taylor polynomial example
Example of a calculating a second-degree multivariable Taylor polynomial. - Historical and theoretical comments: Mean Value Theorem
Comments on the traditional way that Taylor polynomials are taught as inextricably linked with issues about infinite series. - 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. - 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? - 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. - Linear and quadratic Taylor polynomial problems
Sample problems involving first and second order Taylor polynomials. - Solutions to linear and quadratic Taylor polynomial problems
Solutions to sample problems involving first and second order Taylor polynomials.