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Summary Of: Taylor's theorem

Taylor's theorem in one variable... Taylor's theorem for several variables... Taylor's theorem in one variable... Taylor's theorem in one variable... Taylor's theorem in one variable... Taylor's theorem asserts that a function can be approximated by a polynomial... A simple example of application of Taylor's theorem is the approximation of the... Taylor's theorem applies to any sufficiently differentiable function... This exposes Taylor's theorem as a generalization of the... the mean value theorem is used to prove Taylor's theorem with the Lagrange remainder term... This exposes Taylor's theorem as a generalization of the... there is a version of Taylor's theorem for functions in several variables... Another common version of Taylor's theorem holds on an interval... A precise version of Taylor's theorem in this form is as follows... Taylor's theorem for several variables... Taylor's theorem for several variables... Taylor's theorem can be generalized to several variables as follows... Taylor's theorem asserts that for any... Taylor's theorem in one variable... Taylor's theorem in one variable... We first prove Taylor's theorem with the integral remainder term... we may derive Taylor's theorem for higher values... suppose that Taylor's theorem holds for a... variable version of Taylor's theorem to the function...

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The exponential function y = ex (continuous red line) and the corresponding Taylor polynomial of degree four around the origin (dashed green line). | | calculus | differentiable | function | polynomials | Brook Taylor | James Gregory | exponential function | integer | closed interval | open interval | factorial | Lagrange | mean value theorem | Cauchy | Cauchy mean value theorem | integral | absolutely continuous | fundamental theorem of calculus | Taylor series | converge | neighbourhood | analytic | complex | vector | contour integral | uniform estimate | infinitely differentiable | analytic function | uniformly | calculus | Fundamental theorem | Limits of functions | Continuity | Vector calculus | Matrix calculus | Mean value theorem | Differentiation | Product rule | Quotient rule | Chain rule | Change of variables | Implicit differentiation | Related rates | List of differentiation identities | Integration | Lists of integrals | Improper integrals | parts | disks | cylindrical
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| substitution | trigonometric substitution | partial fractions | changing order | ball | closure | multi-index notation | fundamental theorem of calculus | Integration by parts | induction | integration by parts | mean value theorem | Cauchy mean value theorem | chain rule | multinomial coefficient | multi-index | Taylor series | Laurent series | absolutely continuous | fundamental theorem of calculus | almost everywhere | Lebesgue integrals | Apostol, Tom | ISBN 0-471-00005-1 | ISBN 0-486-40453-6 | cut-the-knot | Categories | Calculus | Mathematical theorems | Mathematical series |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Taylor's theorem".