Taylor's theorem

related topics
{math, number, function}
{rate, high, increase}
{area, part, region}

Power rule, Product rule, Quotient rule, Chain rule

Lists of integrals
Improper integrals
Integration by:
parts, disks, cylindrical
, substitution,
trigonometric substitution,
partial fractions, changing order

In calculus, Taylor's theorem gives a sequence of approximations of a differentiable function around a given point by polynomials (the Taylor polynomials of that function) whose coefficients depend only on the derivatives of the function at that point. The theorem also gives precise estimates on the size of the error in the approximation. The theorem is named after the mathematician Brook Taylor, who stated it in 1712, though the result was first discovered 41 years earlier in 1671 by James Gregory.


Taylor's theorem in one variable


Taylor's theorem asserts that any sufficiently smooth function can locally be approximated by polynomials. A simple example of application of Taylor's theorem is the approximation of the exponential function ex near x = 0:

Full article ▸

related documents
Extended Euclidean algorithm
Uniform continuity
Template (programming)
Cholesky decomposition
Metric space
Square root
Hausdorff dimension
Icon (programming language)
Kernel (matrix)
Dirac delta function
Tail recursion
Set (mathematics)
Cantor's diagonal argument
Equivalence relation
Vigenère cipher
Exponential function
Standard ML
Complete metric space
Semidirect product
L'Hôpital's rule
Insertion sort
Riemannian manifold
Communication complexity
Category theory