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In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function , the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.
Examples of functions that are not entire include the square root, the logarithm, the trigonometric function tangent, and its inverse, arctan. For these functions the Taylor series do not converge if x is far from b. That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor ...
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem [1] posed by the 15th-century German mathematician Johannes Müller [2] (also known as Regiomontanus). The problem is as follows: The two dots at eye level are possible locations of the viewer's eye. A painting hangs from a wall.
Milliken–Taylor theorem (Ramsey theory) Milliken's tree theorem (Ramsey theory) Milman–Pettis theorem (Banach space) Min-max theorem (functional analysis) Minimax theorem (game theory) Minkowski's theorem (geometry of numbers) Minkowski's second theorem (geometry of numbers) Minkowski–Hlawka theorem (geometry of numbers) Minlos's theorem ...
Brook Taylor FRS (18 August 1685 – 29 December 1731) was an English mathematician and barrister best known for several results in mathematical analysis. Taylor's most famous developments are Taylor's theorem and the Taylor series, essential in the infinitesimal approach of functions in specific points.
Intuitively, this means that we can express the jet of a curve through p in terms of its Taylor series in local coordinates on M. Examples in local coordinates: As indicated previously, the 1-jet of a curve through p is a tangent vector. A tangent vector at p is a first-order differential operator acting on smooth real-valued functions at p. In ...
When that video raked up hundreds of thousands of views in a matter of days, it inspired him to reimagine other ways to teach math, including using the tune to Swift's "Anti-Hero" to help students ...
The Hales–Jewett theorem implies Van der Waerden's theorem. A theorem similar to van der Waerden's theorem is Schur's theorem : for any given c there is a number N such that if the numbers 1, 2, ..., N are coloured with c different colours, then there must be a pair of integers x , y such that x , y , and x + y are all the same colour.
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