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Taylor Polynomials

  • Kennan T. Smith
Chapter
  • 318 Downloads
Part of the Universitext book series (UTX)

Abstract

THEOREM 1.1 (Mean value theorem) If g and h are continuous on the closed interval I and differentiable on the open interval and a and x are points in I, then there is a point c between a and x such that h’(c)(g(x)−g(a)) = g’(c)(h(x)−h(a)), or \( \frac{{{\text{g}}\left( {\text{x}} \right)\, - \,{\text{g}}\left( {\text{a}} \right)}}{{{\text{h}}\left( {\text{x}} \right) - {\text{h}}\left( {\text{a}} \right)}}\, = \,\frac{{{\text{g}}'\,\left( {\text{c}} \right)}}{{{\text{h}}'\left( {\text{c}} \right)}} \) if the denominators are ≠ 0.

Keywords

TAYLOR Polynomial Complex Derivative Polynomial Part Polynomial Answer Simpson Integra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Kennan T. Smith
    • 1
  1. 1.Mathematics DepartmentOregon State UniversityCorvallisUSA

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