Search results
Results from the WOW.Com Content Network
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.
That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...
In mathematics, the branch of real analysis studies the behavior of real numbers, ... Taylor's theorem, the fundamental theorem of calculus, ...
Pages in category "Theorems in real analysis" The following 45 pages are in this category, out of 45 total. ... Taylor's theorem; Titchmarsh convolution theorem; U.
In mathematics, Hadamard's lemma, named after Jacques Hadamard, is essentially a first-order form of Taylor's theorem, in which we can express a smooth, real-valued function exactly in a convenient manner.
Darboux's theorem (analysis) ... Inverse function theorem; L. ... Taylor's theorem; Triple product rule; U. Uniqueness theorem for Poisson's equation
Taylor's theorem – gives an approximation of a times differentiable function around a given point by a -th order Taylor-polynomial. L'Hôpital's rule – uses derivatives to help evaluate limits involving indeterminate forms; Abel's theorem – relates the limit of a power series to the sum of its coefficients
Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case = states that = + ′ () + where is the remainder term. The linear approximation is obtained by dropping the remainder: () + ′ ().