Meaning of Taylor polynomial | Babel Free

Definitions

A truncated Taylor series; the sum of the first n terms of a Taylor series.

Equivalents

Examples

“For example, if Mⁿ#61;#92;mathbb#123;R#125;ⁿ and Nᵏ#61;#92;mathbb#123;R#125;, a singularity means the vanishing of the gradient, or equivalently, the linear terms of the Taylor's polynomial of some degree greater than 1. If one has a singularity, one may look⟳ at the second-order terms in the Taylor's polynomial.”

“The polynomial approximation above for exp(x) is an example of a Taylor polynomial of degree 2 and in fact the polynomial approximations to sin(x) and cos(x) that we wrote down in Chapter 3 are also Taylor polynomials.”

“Then, we introduce⟳ and investigate⟳ the Taylor polynomials and we prove⟳ suitable versions of the Lagrange mean⟳ value theorem and of the Taylor formula.”

CEFR level